Edit Profile (opens in new tab) Kallianpur, Gopinath (b. 1925 d. 2015) Co-Author Distance Author ID: kallianpur.gopinath Published as: Kallianpur, Gopinath; Kallianpur, G. External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef Documents Indexed: 137 Publications since 1951, including 6 Books 4 Contributions as Editor · 1 Further Contribution Biographic References: 3 Publications Co-Authors: 44 Co-Authors with 101 Joint Publications 1,193 Co-Co-Authors all top 5 Co-Authors 40 single-authored 17 Karandikar, Rajeeva Laxman 10 Xiong, Jie 9 Mandrekar, Vidyadhar S. 6 Budhiraja, Amarjit S. 6 Johnson, Gerald William 4 Striebel, Charlotte T. 4 Sundar, Padmanabhan 3 Dasgupta, Amites 3 Hu, Yaozhong 3 Jain, Naresh C. 3 Oodaira, Hiroshi 3 Pérez-Abreu Carrión, Víctor M. 3 Wolpert, Robert L. 2 Bhatt, Abhay G. 2 Bromley, C. 2 Chiang, Tzuu-Shuh 2 Fujisaki, Masatoshi 2 Hida, Takeyuki 2 Hucke, Hans-Peter 2 Kunita, Hiroshi 2 Mitoma, Itaru 2 Oleĭnik, Ol’ga Arsen’evna 2 Robbins, Herbert Ellis 1 Amirdjanova, Anna 1 Belyaev, Yuriĭ Konstantinovich 1 Bode, H. W. 1 Borwanker, J. D. 1 Bucy, Richard S. 1 Christensen, S. K. 1 Ephremides, Anthony 1 Etemadi, Nasrollah 1 Farshidi, Jamshid 1 Ghosh, Jayanta Kumar 1 Hanner, Olof 1 Hurd, Harry L. 1 Kadota, T. T. 1 Kailath, Thomas 1 Kalman, Rudolf Emil 1 Kölzow, Dietrich 1 Korezlioglu, Hayri 1 Krishnaiah, Paruchuri Rama 1 Kuo, Hui-Hsiung 1 Lévy, Paul 1 Miamee, Abol G. 1 Nadkarni, Mahendra G. 1 Niemi, Hannu 1 Papanicolaou, Vassilis G. 1 Prakasa Rao, B. L. S. 1 Ramachandran, Doraiswamy 1 Rao, Calyampudi Radhakrishna 1 Rozdnov, Ju. A. 1 Selukar, R. S. 1 Shannon, G. E. 1 Shepp, Lawrence Alan 1 Thomas, John Bowman 1 Triggiani, Roberto 1 Ustunel, Ali Suleyman all top 5 Serials 18 Applied Mathematics and Optimization 6 Journal of Multivariate Analysis 6 Annals of Mathematical Statistics 5 The Annals of Probability 3 Theory of Probability and its Applications 3 Sankhyā. Series A. Methods and Techniques 3 Stochastics and Stochastics Reports 2 Russian Mathematical Surveys 2 Teoriya Veroyatnosteĭ i eë Primeneniya 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Acta Applicandae Mathematicae 2 Probability Theory and Related Fields 2 Stochastic Processes and their Applications 1 Advances in Applied Probability 1 Doklady Akademii Nauk SSSR 1 Mathematical Biosciences 1 Stochastics 1 Arkiv för Matematik 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Nagoya Mathematical Journal 1 Osaka Journal of Mathematics 1 Probability and Mathematical Statistics 1 American Journal of Mathematical and Management Sciences 1 The Annals of Applied Probability 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Statistica Sinica 1 Infinite Dimensional Analysis, Quantum Probability and Related Topics 1 Stochastic Environmental Research and Risk Assessment 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Paris 1 Journal of Mathematics and Mechanics 1 Sankhyā 1 Institute of Mathematical Statistics Lecture Notes - Monograph Series 1 Lecture Notes in Biomathematics 1 Lecture Notes in Control and Information Sciences 1 Lecture Notes in Mathematics 1 Stochastics Monographs 1 Oxford Graduate Texts in Mathematics 1 Applications of Mathematics all top 5 Fields 117 Probability theory and stochastic processes (60-XX) 28 Systems theory; control (93-XX) 15 Statistics (62-XX) 9 Measure and integration (28-XX) 7 Quantum theory (81-XX) 6 Functional analysis (46-XX) 5 Biology and other natural sciences (92-XX) 4 General and overarching topics; collections (00-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Partial differential equations (35-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Operator theory (47-XX) 1 Special functions (33-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Numerical analysis (65-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 97 Publications have been cited 1,252 times in 971 Documents Cited by ▼ Year ▼ Stochastic filtering theory. Zbl 0458.60001 Kallianpur, Gopinath 207 1980 Stochastic differential equations for the non linear filtering problem. Zbl 0242.93051 Fujisaki, Masatoshi; Kallianpur, Gopinath; Kunita, Hiroshi 79 1972 Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures. Zbl 0845.60008 Kallianpur, G.; Xiong, J. 49 1995 Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors. Zbl 0174.22102 Kallianpur, Gopinath; Striebel, C. 46 1968 Stochastic differential equations in infinite dimensional spaces. Expanded version of the lectures delivered as part of the 1993 Barrett Lectures at the University of Tennessee, Knoxville, TN, USA, March 25–27, 1993. Zbl 0859.60050 Kallianpur, Gopinath; Xiong, Jie 43 1996 Ergodic property of the Brownian motion process. Zbl 0053.10003 Kallianpur, Gopinath; Robbins, H. 33 1953 Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula. Zbl 0583.60049 Kallianpur, Gopinath; Kannan, D.; Karandikar, R. L. 30 1985 Stochastic evolution equations driven by nuclear-space-valued martingales. Zbl 0643.60049 Kallianpur, G.; Perez-Abreu, V. 29 1988 Generalized Feynman integrals using analytic continuation in several complex variables. Zbl 0554.60061 Kallianpur, Gopinath; Bromley, C. 28 1984 Zero-one laws for Gaussian processes. Zbl 0234.60032 Kallianpur, Gopinath 26 1970 Infinite dimensional stochastic differential equation models for spatially distributed neurons. Zbl 0565.60055 Kallianpur, Gopinath; Wolpert, R. 26 1984 Large deviations for a class of stochastic partial differential equations. Zbl 0854.60026 Kallianpur, Gopinath; Xiong, Jie 25 1996 Abstract Wiener processes and their reproducing kernel Hilbert spaces. Zbl 0194.49003 Kallianpur, Gopinath 25 1971 The sequence of sums of independent random variables. Zbl 0055.36704 Kallianpur, Gopinath; Robbins, H. 23 1954 Multiple fractional integrals. Zbl 0948.60022 Dasgupta, A.; Kallianpur, G. 21 1999 Schrödinger equations with fractional Laplacians. Zbl 1002.60048 Hu, Y.; Kallianpur, G. 21 2000 Homogeneous chaos, \(p\)-forms, scaling and the Feynman integral. Zbl 0784.60056 Johnson, G. W.; Kallianpur, G. 21 1993 Chaos decomposition of multiple fractional integrals and applications. Zbl 0952.60043 Dasgupta, A.; Kallianpur, G. 20 1999 Nondeterministic random fields and Wold and Halmos decompositions for commuting isometries. Zbl 0522.60050 Kallianpur, Gopinath; Mandrekar, V. 19 1983 On the prediction theory of two-parameter stationary random fields. Zbl 0726.60051 Kallianpur, G.; Miamee, A. G.; Niemi, H. 17 1990 The Bernstein-von Mises theorem for Markov processes. Zbl 0245.62075 Borwanker, J.; Kallianpur, Gopinath; Prakasa Rao, B. L. S. 17 1971 Introduction to option pricing theory. Zbl 0969.91003 Kallianpur, Gopinath; Karandikar, Rajeeva L. 16 2000 Arbitrage opportunities for a class of Gladyshev processes. Zbl 0960.91053 Dasgupta, A.; Kallianpur, G. 15 2000 Approximations to the solution of the Zakai equation using multiple Wiener and Stratonovich integral expansions. Zbl 0912.60059 Budhiraja, A.; Kallianpur, G. 15 1996 A finitely additive white noise approach to nonlinear filtering. Zbl 0525.93063 Kallianpur, Gopinath; Karandikar, R. L. 15 1983 The Markov property for generalized Gaussian random fields. Zbl 0275.60054 Kallianpur, Gopinath; Mandrekar, V. 14 1974 Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering. Zbl 0861.60051 Bhatt, Abhay G.; Kallianpur, G.; Karandikar, Rajeeva L. 14 1995 On the diffusion approximation to a discontinuous model for a single neuron. Zbl 0526.92009 Kallianpur, Gopinath 13 1983 Spectral theory of stationary \({\mathcal H}\)-valued processes. Zbl 0248.60028 Kallianpur, Gopinath; Mandrekar, V. 13 1971 An approximation for the Zakai equation. Zbl 1001.60044 Hu, Y.; Kallianpur, G.; Xiong, J. 12 2002 Diffusion equations in duals of nuclear spaces. Zbl 0702.60056 Kallianpur, G.; Mitoma, I.; Wolpert, R. L. 12 1990 Exponential integrability and application to stochastic quantization. Zbl 0903.60046 Hu, Y.; Kallianpur, G. 12 1998 Multiplicity and representation theory of purely non-deterministic stochastic processes. Zbl 0171.38902 Kallianpur, Gopinath; Mandrekar, V. 12 1965 White noise theory of prediction, filtering and smoothing. Zbl 0724.93076 Kallianpur, Gopinath; Karandikar, Rajeeva L. 12 1988 White noise calculus and nonlinear filtering theory. Zbl 0584.60055 Kallianpur, Gopinath; Karandikar, R. L. 11 1985 Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Zbl 0195.44503 Kallianpur, Gopinath; Striebel, C. 11 1969 Stochastic analysis and diffusion processes. Zbl 1303.60003 Kallianpur, Gopinath; Sundar, P. 11 2014 A note on uniform convergence of stochastic processes. Zbl 0232.60040 Jain, Naresh C.; Kallianpur, Gopinath 10 1970 Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces. Zbl 0743.60108 Chiang, T. S.; Kallianpur, G.; Sundar, P. 10 1991 Parameter estimation in linear filtering. Zbl 0768.62086 Kallianpur, G.; Selukar, R. S. 10 1991 Non-anticipative representations of equivalent Gaussian processes. Zbl 0293.60030 Kallianpur, Gopinath; Oodaira, Hiroshi 9 1973 Robustness of the nonlinear filter. Zbl 0963.60039 Bhatt, Abhay G.; Kallianpur, G.; Karandikar, Rajeeva L. 9 1999 Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Zbl 0208.43703 Kallianpur, Gopinath; Striebel, C. 9 1969 Norm convergent expansions for Gaussian processes in Banach spaces. Zbl 0209.48604 Jain, Naresh C.; Kallianpur, Gopinath 9 1970 The equivalence and singularity of Gaussian measures. Zbl 0288.60039 Kallianpur, Gopinath; Oodaira, Hiroshi 8 1963 The role of reproducing kernel Hilbert spaces in the study of Gaussian processes. Zbl 0234.60058 Kallianpur, Gopinath 8 1970 Oscillation function o f a multiparameter Gaussian process. Zbl 0249.60016 Jain, Naresh C.; Kallianpur, Gopinath 8 1972 Freidlin-Wentzell type estimates for abstract Wiener spaces. Zbl 0419.60035 Kallianpur, Gopinath; Oodaira, Hiroshi 7 1978 Measure-valued equations for the optimum filter in finitely additive nonlinear filtering theory. Zbl 0592.93060 Kallianpur, Gopinath; Karandikar, R. L. 7 1984 Nonanticipative transformations of the two-parameter Wiener process and a Girsanov theorem. Zbl 0382.60039 Etemadi, N.; Kallianpur, Gopinath 6 1977 On Fisher’s lower bound to asymptotic variance of a consistent estimate. Zbl 0067.37301 Kallianpur, Gopinath; Radhakrishna Rao, C. 6 1955 Stochastic models of environmental pollution. Zbl 0804.60041 Kallianpur, G.; Xiong, J. 5 1994 The existence and uniqueness of solutions of nuclear space-valued stochastic differential equations driven by Poisson random measures. Zbl 0831.60064 Kallianpur, G.; Xiong, J.; Hardy, G.; Ramasubramanian, S. 5 1994 Correlation and spectral theory for periodically correlated random fields indexed on \(\mathbb Z^{2}\). Zbl 1053.60050 Hurd, H.; Kallianpur, G.; Farshidi, J. 5 2004 The nonlinear filtering problem for the unbounded case. Zbl 0571.60055 Kallianpur, Gopinath; Karandikar, R. L. 5 1984 The topology of weak convergence of probability measures. Zbl 0272.60004 Kallianpur, Gopinath 4 1961 The square of a Gaussian Markov process and nonlinear prediction. Zbl 0331.60024 Hida, T.; Kallianpur, Gopinath 4 1975 Weak convergence of stochastic neuronal models. Zbl 0641.92009 Kallianpur, G.; Wolpert, Robert L. 4 1987 Stochastic filtering theory. (Stokhasticheskaya teoriya fil’tratsii). Transl. from English by V. M. Shurenkov. Transl. ed. by A. V. Skorokhod. Zbl 0644.60037 Kallianpur, Gopinath 4 1987 Two results on multiple Stratonovich integrals. Zbl 1002.60544 Budhiraja, A.; Kallianpur, G. 4 1997 Infinite dimensional stochastic differential equations with applications. Zbl 0818.60048 Kallianpur, Gopinath 4 1990 Semi-groups of isometries and the representation and multiplicity of weakly stationary stochastic processes. Zbl 0171.38803 Kallianpur, Gopinath; Mandrekar, V. 4 1966 Regularity property of Donsker’s delta function. Zbl 0552.60035 Kallianpur, Gopinath; Kuo, Hui-Hsiung 4 1984 Some remarks on Hu and Meyer’s paper and infinite-dimensional calculus on finitely additive canonical Hilbert space. Zbl 0766.60061 Johnson, G. W.; Kallianpur, G. 4 1989 A nuclear space-valued stochastic differential equation driven by Poisson random measures. Zbl 0766.60076 Kallianpur, G.; Xiong, J. 4 1992 A problem in optimum filtering with finite data. Zbl 0096.33704 Kallianpur, Gopinath 4 1959 The Feynman-Stratonovich semigroup and Stratonovich integral expansions in nonlinear filtering. Zbl 0872.60042 Budhiraja, A.; Kallianpur, G. 3 1997 Asset pricing with stochastic volatility. Zbl 1013.91040 Kallianpur, G.; Xiong, J. 3 2001 The filtering problem for infinite dimensional stochastic processes. Zbl 0649.93070 Kallianpur, G.; Karandikar, R. L. 3 1988 Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures. Zbl 0823.60047 Kallianpur, G.; Xiong, J. 3 1994 Von Mises functionals and maximum likelihood estimation. Zbl 0129.32404 Kallianpur, Gopinath 3 1963 Some recent developments in nonlinear filtering theory. Zbl 0533.60049 Kallianpur, Gopinath; Karandikar, R. L. 3 1983 A Segal-Langevin type stochastic differential equation on a space of generalized functionals. Zbl 0764.46040 Kallianpur, Gopinath; Mitoma, Itaru 3 1992 A note on the Robbins-Monro stochastic approximation method. Zbl 0055.37807 Kallianpur, Gopinath 3 1954 Gaussian random fields. Zbl 0443.60034 Bromley, C.; Kallianpur, Gopinath 2 1980 A curious example from statistical differential geometry. Zbl 0963.62003 Kallianpur, G.; Kim, Y.-T. 2 1998 Supports of Gaussian measures. Zbl 0268.60041 Kallianpur, Gopinath; Nadkarni, M. 2 1972 Weak convergence of solutions of stochastic evolution equations on nuclear spaces. Zbl 0695.60064 Kallianpur, G.; Pérez-Abreu, V. 2 1989 A skeletal theory of filtering. Zbl 0732.60051 Kallianpur, G. 2 1991 Nonlinear transformations of the canonical Gauss measure on Hilbert space and absolute continuity. Zbl 0803.60050 Kallianpur, G.; Karandikar, R. L. 2 1994 Traces, natural extensions and Feynman distributions. Zbl 0823.46046 Kallianpur, G. 2 1991 Statistics and probability: Essays in Honor of C. R. Rao. Zbl 0474.00011 2 1982 The Skorohod integral and the derivative operator of functionals of a cylindrical Brownian motion. Zbl 0754.60052 Kallianpur, G.; Pérez-Abreu, V. 2 1992 The generalized Hu-Meyer formula for random kernels. Zbl 0876.60029 Budhiraja, A.; Kallianpur, G. 2 1997 The Markov property of the filter in the finitely additive white noise approach to nonlinear filtering. Zbl 0543.60051 Kallianpur, Gopinath; Karandikar, R. L. 2 1984 Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems. Zbl 0777.92004 Kallianpur, Gopinath 2 1992 A note on perfect probability. Zbl 0093.14304 Kallianpur, Gopinath 2 1959 Stochastic Dyson series and the solution to associated stochastic evolution equations. Zbl 0936.60050 Johnson, G. W.; Kallianpur, G. 1 1998 Random processes. Multiplicity theory and canonical decompositions. Zbl 0364.60005 1 1973 Hilbert space valued traces and multiple Stratonovich integrals with statistical applications. Zbl 0815.60047 Budhiraja, A.; Kallianpur, G. 1 1994 Stochastic differential equations in infinite dimensions: A brief survey and some new directions of research. Zbl 0786.60081 Kallianpur, G.; Xiong, J. 1 1993 Multiple Wiener integrals on abstract Wiener spaces and liftings of \(p\)- linear forms. Zbl 0818.60043 Johnson, G. W.; Kallianpur, G. 1 1990 Remarks on the existence of \(k\)-traces. Zbl 0857.60050 Johnson, Gerald W.; Kallianpur, Gopinath 1 1994 Hilbert space valued traces and multiple Stratonovich integrals with statistical applications. Zbl 0861.60068 Budhiraja, A.; Kallianpur, G. 1 1995 Commuting semigroups of isometries and Karhunen representation of second order stationary random fields. Zbl 0514.60047 Kallianpur, Gopinath; Mandrekar, V. 1 1983 The analytic Feynman integral of the natural extension of \(p\)th homogeneous chaos. Zbl 0773.60041 Johnson, G. W.; Kallianpur, G. 1 1992 On the amount of information contained in a \(\sigma\)-field. Zbl 0099.34303 Kallianpur, Gopinath 1 1960 Stochastic analysis and diffusion processes. Zbl 1303.60003 Kallianpur, Gopinath; Sundar, P. 11 2014 Correlation and spectral theory for periodically correlated random fields indexed on \(\mathbb Z^{2}\). Zbl 1053.60050 Hurd, H.; Kallianpur, G.; Farshidi, J. 5 2004 An approximation for the Zakai equation. Zbl 1001.60044 Hu, Y.; Kallianpur, G.; Xiong, J. 12 2002 Asset pricing with stochastic volatility. Zbl 1013.91040 Kallianpur, G.; Xiong, J. 3 2001 Schrödinger equations with fractional Laplacians. Zbl 1002.60048 Hu, Y.; Kallianpur, G. 21 2000 Introduction to option pricing theory. Zbl 0969.91003 Kallianpur, Gopinath; Karandikar, Rajeeva L. 16 2000 Arbitrage opportunities for a class of Gladyshev processes. Zbl 0960.91053 Dasgupta, A.; Kallianpur, G. 15 2000 Multiple fractional integrals. Zbl 0948.60022 Dasgupta, A.; Kallianpur, G. 21 1999 Chaos decomposition of multiple fractional integrals and applications. Zbl 0952.60043 Dasgupta, A.; Kallianpur, G. 20 1999 Robustness of the nonlinear filter. Zbl 0963.60039 Bhatt, Abhay G.; Kallianpur, G.; Karandikar, Rajeeva L. 9 1999 Exponential integrability and application to stochastic quantization. Zbl 0903.60046 Hu, Y.; Kallianpur, G. 12 1998 A curious example from statistical differential geometry. Zbl 0963.62003 Kallianpur, G.; Kim, Y.-T. 2 1998 Stochastic Dyson series and the solution to associated stochastic evolution equations. Zbl 0936.60050 Johnson, G. W.; Kallianpur, G. 1 1998 Two results on multiple Stratonovich integrals. Zbl 1002.60544 Budhiraja, A.; Kallianpur, G. 4 1997 The Feynman-Stratonovich semigroup and Stratonovich integral expansions in nonlinear filtering. Zbl 0872.60042 Budhiraja, A.; Kallianpur, G. 3 1997 The generalized Hu-Meyer formula for random kernels. Zbl 0876.60029 Budhiraja, A.; Kallianpur, G. 2 1997 Stochastic differential equations in infinite dimensional spaces. Expanded version of the lectures delivered as part of the 1993 Barrett Lectures at the University of Tennessee, Knoxville, TN, USA, March 25–27, 1993. Zbl 0859.60050 Kallianpur, Gopinath; Xiong, Jie 43 1996 Large deviations for a class of stochastic partial differential equations. Zbl 0854.60026 Kallianpur, Gopinath; Xiong, Jie 25 1996 Approximations to the solution of the Zakai equation using multiple Wiener and Stratonovich integral expansions. Zbl 0912.60059 Budhiraja, A.; Kallianpur, G. 15 1996 Diffusion approximation of nuclear space-valued stochastic differential equations driven by Poisson random measures. Zbl 0845.60008 Kallianpur, G.; Xiong, J. 49 1995 Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering. Zbl 0861.60051 Bhatt, Abhay G.; Kallianpur, G.; Karandikar, Rajeeva L. 14 1995 Hilbert space valued traces and multiple Stratonovich integrals with statistical applications. Zbl 0861.60068 Budhiraja, A.; Kallianpur, G. 1 1995 Stochastic models of environmental pollution. Zbl 0804.60041 Kallianpur, G.; Xiong, J. 5 1994 The existence and uniqueness of solutions of nuclear space-valued stochastic differential equations driven by Poisson random measures. Zbl 0831.60064 Kallianpur, G.; Xiong, J.; Hardy, G.; Ramasubramanian, S. 5 1994 Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures. Zbl 0823.60047 Kallianpur, G.; Xiong, J. 3 1994 Nonlinear transformations of the canonical Gauss measure on Hilbert space and absolute continuity. Zbl 0803.60050 Kallianpur, G.; Karandikar, R. L. 2 1994 Hilbert space valued traces and multiple Stratonovich integrals with statistical applications. Zbl 0815.60047 Budhiraja, A.; Kallianpur, G. 1 1994 Remarks on the existence of \(k\)-traces. Zbl 0857.60050 Johnson, Gerald W.; Kallianpur, Gopinath 1 1994 Homogeneous chaos, \(p\)-forms, scaling and the Feynman integral. Zbl 0784.60056 Johnson, G. W.; Kallianpur, G. 21 1993 Stochastic differential equations in infinite dimensions: A brief survey and some new directions of research. Zbl 0786.60081 Kallianpur, G.; Xiong, J. 1 1993 A nuclear space-valued stochastic differential equation driven by Poisson random measures. Zbl 0766.60076 Kallianpur, G.; Xiong, J. 4 1992 A Segal-Langevin type stochastic differential equation on a space of generalized functionals. Zbl 0764.46040 Kallianpur, Gopinath; Mitoma, Itaru 3 1992 The Skorohod integral and the derivative operator of functionals of a cylindrical Brownian motion. Zbl 0754.60052 Kallianpur, G.; Pérez-Abreu, V. 2 1992 Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems. Zbl 0777.92004 Kallianpur, Gopinath 2 1992 The analytic Feynman integral of the natural extension of \(p\)th homogeneous chaos. Zbl 0773.60041 Johnson, G. W.; Kallianpur, G. 1 1992 Propagation of chaos and the McKean-Vlasov equation in duals of nuclear spaces. Zbl 0743.60108 Chiang, T. S.; Kallianpur, G.; Sundar, P. 10 1991 Parameter estimation in linear filtering. Zbl 0768.62086 Kallianpur, G.; Selukar, R. S. 10 1991 A skeletal theory of filtering. Zbl 0732.60051 Kallianpur, G. 2 1991 Traces, natural extensions and Feynman distributions. Zbl 0823.46046 Kallianpur, G. 2 1991 On the prediction theory of two-parameter stationary random fields. Zbl 0726.60051 Kallianpur, G.; Miamee, A. G.; Niemi, H. 17 1990 Diffusion equations in duals of nuclear spaces. Zbl 0702.60056 Kallianpur, G.; Mitoma, I.; Wolpert, R. L. 12 1990 Infinite dimensional stochastic differential equations with applications. Zbl 0818.60048 Kallianpur, Gopinath 4 1990 Multiple Wiener integrals on abstract Wiener spaces and liftings of \(p\)- linear forms. Zbl 0818.60043 Johnson, G. W.; Kallianpur, G. 1 1990 Some remarks on Hu and Meyer’s paper and infinite-dimensional calculus on finitely additive canonical Hilbert space. Zbl 0766.60061 Johnson, G. W.; Kallianpur, G. 4 1989 Weak convergence of solutions of stochastic evolution equations on nuclear spaces. Zbl 0695.60064 Kallianpur, G.; Pérez-Abreu, V. 2 1989 Stochastic evolution equations driven by nuclear-space-valued martingales. Zbl 0643.60049 Kallianpur, G.; Perez-Abreu, V. 29 1988 White noise theory of prediction, filtering and smoothing. Zbl 0724.93076 Kallianpur, Gopinath; Karandikar, Rajeeva L. 12 1988 The filtering problem for infinite dimensional stochastic processes. Zbl 0649.93070 Kallianpur, G.; Karandikar, R. L. 3 1988 Weak convergence of stochastic neuronal models. Zbl 0641.92009 Kallianpur, G.; Wolpert, Robert L. 4 1987 Stochastic filtering theory. (Stokhasticheskaya teoriya fil’tratsii). Transl. from English by V. M. Shurenkov. Transl. ed. by A. V. Skorokhod. Zbl 0644.60037 Kallianpur, Gopinath 4 1987 Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces, and a Cameron-Martin formula. Zbl 0583.60049 Kallianpur, Gopinath; Kannan, D.; Karandikar, R. L. 30 1985 White noise calculus and nonlinear filtering theory. Zbl 0584.60055 Kallianpur, Gopinath; Karandikar, R. L. 11 1985 Generalized Feynman integrals using analytic continuation in several complex variables. Zbl 0554.60061 Kallianpur, Gopinath; Bromley, C. 28 1984 Infinite dimensional stochastic differential equation models for spatially distributed neurons. Zbl 0565.60055 Kallianpur, Gopinath; Wolpert, R. 26 1984 Measure-valued equations for the optimum filter in finitely additive nonlinear filtering theory. Zbl 0592.93060 Kallianpur, Gopinath; Karandikar, R. L. 7 1984 The nonlinear filtering problem for the unbounded case. Zbl 0571.60055 Kallianpur, Gopinath; Karandikar, R. L. 5 1984 Regularity property of Donsker’s delta function. Zbl 0552.60035 Kallianpur, Gopinath; Kuo, Hui-Hsiung 4 1984 The Markov property of the filter in the finitely additive white noise approach to nonlinear filtering. Zbl 0543.60051 Kallianpur, Gopinath; Karandikar, R. L. 2 1984 Nondeterministic random fields and Wold and Halmos decompositions for commuting isometries. Zbl 0522.60050 Kallianpur, Gopinath; Mandrekar, V. 19 1983 A finitely additive white noise approach to nonlinear filtering. Zbl 0525.93063 Kallianpur, Gopinath; Karandikar, R. L. 15 1983 On the diffusion approximation to a discontinuous model for a single neuron. Zbl 0526.92009 Kallianpur, Gopinath 13 1983 Some recent developments in nonlinear filtering theory. Zbl 0533.60049 Kallianpur, Gopinath; Karandikar, R. L. 3 1983 Commuting semigroups of isometries and Karhunen representation of second order stationary random fields. Zbl 0514.60047 Kallianpur, Gopinath; Mandrekar, V. 1 1983 Statistics and probability: Essays in Honor of C. R. Rao. Zbl 0474.00011 2 1982 Stochastic filtering theory. Zbl 0458.60001 Kallianpur, Gopinath 207 1980 Gaussian random fields. Zbl 0443.60034 Bromley, C.; Kallianpur, Gopinath 2 1980 Freidlin-Wentzell type estimates for abstract Wiener spaces. Zbl 0419.60035 Kallianpur, Gopinath; Oodaira, Hiroshi 7 1978 Nonanticipative transformations of the two-parameter Wiener process and a Girsanov theorem. Zbl 0382.60039 Etemadi, N.; Kallianpur, Gopinath 6 1977 The square of a Gaussian Markov process and nonlinear prediction. Zbl 0331.60024 Hida, T.; Kallianpur, Gopinath 4 1975 The Markov property for generalized Gaussian random fields. Zbl 0275.60054 Kallianpur, Gopinath; Mandrekar, V. 14 1974 Non-anticipative representations of equivalent Gaussian processes. Zbl 0293.60030 Kallianpur, Gopinath; Oodaira, Hiroshi 9 1973 Random processes. Multiplicity theory and canonical decompositions. Zbl 0364.60005 1 1973 Stochastic differential equations for the non linear filtering problem. Zbl 0242.93051 Fujisaki, Masatoshi; Kallianpur, Gopinath; Kunita, Hiroshi 79 1972 Oscillation function o f a multiparameter Gaussian process. Zbl 0249.60016 Jain, Naresh C.; Kallianpur, Gopinath 8 1972 Supports of Gaussian measures. Zbl 0268.60041 Kallianpur, Gopinath; Nadkarni, M. 2 1972 Abstract Wiener processes and their reproducing kernel Hilbert spaces. Zbl 0194.49003 Kallianpur, Gopinath 25 1971 The Bernstein-von Mises theorem for Markov processes. Zbl 0245.62075 Borwanker, J.; Kallianpur, Gopinath; Prakasa Rao, B. L. S. 17 1971 Spectral theory of stationary \({\mathcal H}\)-valued processes. Zbl 0248.60028 Kallianpur, Gopinath; Mandrekar, V. 13 1971 Zero-one laws for Gaussian processes. Zbl 0234.60032 Kallianpur, Gopinath 26 1970 A note on uniform convergence of stochastic processes. Zbl 0232.60040 Jain, Naresh C.; Kallianpur, Gopinath 10 1970 Norm convergent expansions for Gaussian processes in Banach spaces. Zbl 0209.48604 Jain, Naresh C.; Kallianpur, Gopinath 9 1970 The role of reproducing kernel Hilbert spaces in the study of Gaussian processes. Zbl 0234.60058 Kallianpur, Gopinath 8 1970 Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Zbl 0195.44503 Kallianpur, Gopinath; Striebel, C. 11 1969 Stochastic differential equations occurring in the estimation of continuous parameter stochastic processes. Zbl 0208.43703 Kallianpur, Gopinath; Striebel, C. 9 1969 Estimation of stochastic systems: Arbitrary system process with additive white noise observation errors. Zbl 0174.22102 Kallianpur, Gopinath; Striebel, C. 46 1968 Semi-groups of isometries and the representation and multiplicity of weakly stationary stochastic processes. Zbl 0171.38803 Kallianpur, Gopinath; Mandrekar, V. 4 1966 Multiplicity and representation theory of purely non-deterministic stochastic processes. Zbl 0171.38902 Kallianpur, Gopinath; Mandrekar, V. 12 1965 The equivalence and singularity of Gaussian measures. Zbl 0288.60039 Kallianpur, Gopinath; Oodaira, Hiroshi 8 1963 Von Mises functionals and maximum likelihood estimation. Zbl 0129.32404 Kallianpur, Gopinath 3 1963 The topology of weak convergence of probability measures. Zbl 0272.60004 Kallianpur, Gopinath 4 1961 On the amount of information contained in a \(\sigma\)-field. Zbl 0099.34303 Kallianpur, Gopinath 1 1960 A problem in optimum filtering with finite data. Zbl 0096.33704 Kallianpur, Gopinath 4 1959 A note on perfect probability. Zbl 0093.14304 Kallianpur, Gopinath 2 1959 On Fisher’s lower bound to asymptotic variance of a consistent estimate. Zbl 0067.37301 Kallianpur, Gopinath; Radhakrishna Rao, C. 6 1955 The sequence of sums of independent random variables. Zbl 0055.36704 Kallianpur, Gopinath; Robbins, H. 23 1954 A note on the Robbins-Monro stochastic approximation method. Zbl 0055.37807 Kallianpur, Gopinath 3 1954 Ergodic property of the Brownian motion process. Zbl 0053.10003 Kallianpur, Gopinath; Robbins, H. 33 1953 all cited Publications top 5 cited Publications all top 5 Cited by 1,119 Authors 24 Kallianpur, Gopinath 19 Xiong, Jie 18 Albeverio, Sergio A. 16 Karandikar, Rajeeva Laxman 15 Mandrekar, Vidyadhar S. 11 Choi, Jae Gil 11 Siu, Tak Kuen 10 Budhiraja, Amarjit S. 9 Hu, Yaozhong 9 Rajeev, Bhaskaran 8 Bojdecki, Tomasz 8 Prakasa Rao, B. L. S. 8 Proske, Frank Norbert 7 Bagchi, Arunabha 7 Cho, Dong Hyun 7 Del Moral, Pierre 7 Kim, Byoung Soo 7 Mohan, Manil Thankamani 7 Pérez-Abreu Carrión, Víctor M. 7 Röckner, Michael 7 Tjøstheim, Dag B. 7 Tudor, Constantin 7 Yoo, Il 6 Ceci, Claudia 6 Chang, Kun Soo 6 Chang, Seung Jun 6 Colaneri, Katia 6 Fonseca-Mora, Christian A. 6 Gorostiza, Luis G. 6 Kouritzin, Michael A. 6 Meyer-Brandis, Thilo 6 Nualart, David 6 Sundar, Padmanabhan 5 Amirdjanova, Anna 5 Bao, Feng 5 Bhatt, Abhay G. 5 Elliott, Robert James 5 Heunis, Andrew J. 5 Jakubowski, Jacek 5 Jolis, Maria 5 Mazzucchi, Sonia 5 Øksendal, Bernt Karsten 5 Roy, Debasish 5 Zhang, Tusheng S. 4 Basin, Michael V. 4 Bhar, Suprio 4 Bînzar, Tudor 4 Crisan, Dan O. 4 Francos, Joseph M. 4 Guasoni, Paolo 4 Jain, Naresh C. 4 Karatzas, Ioannis 4 Korezlioglu, Hayri 4 Krylov, Nicolaĭ Vladimirovich 4 Kuznetsov, Dmitriĭ Feliksovich 4 Lăzureanu, Cristian 4 Leonenko, Nikolai N. 4 Lototsky, Sergey V. 4 Nappo, Giovanna 4 Riedle, Markus 4 Russo, Francesco 4 Salins, Michael 4 Sarkar, Saikat 4 Skoug, David 4 Sun, Wei 4 Szpirglas, Jacques 4 Tudor, Maria 4 Ustunel, Ali Suleyman 4 Vasu, Ram Mohan 4 Yan, Jia-An 4 Yau, Stephen Shing-Toung 3 Athreya, Krishna Balasundaram 3 Bingham, Nicholas Hugh 3 Brody, Dorje C. 3 Brzeźniak, Zdzisław 3 Cambanis, Stamatis 3 Cao, Yanzhao 3 Chen-Charpentier, Benito Miguel 3 Csörgő, Miklós 3 Duan, Jinqiao 3 Dupuis, Paul G. 3 Florchinger, Patrick 3 Gao, Hongjun 3 Ghosh, Mrinal Kanti 3 Goswami, Anindya 3 Hausenblas, Erika 3 Högele, Michael Anton 3 Hucke, Hans-Peter 3 Kleptsyna, Marina L. 3 Kloeden, Peter Eris 3 Kushner, Harold J. 3 Lanconelli, Alberto 3 Lee, Yuhjia 3 LePage, Raoul D. 3 Lo, James Ting-Ho 3 Long, Hongwei 3 Maroulas, Vasileios 3 Mazziotto, Gerald 3 Mishura, Yuliya Stepanivna 3 Moklyachuk, Mykhaĭlo Pavlovych ...and 1,019 more Authors all top 5 Cited in 251 Serials 80 Stochastic Processes and their Applications 39 Journal of Multivariate Analysis 38 Applied Mathematics and Optimization 35 Stochastic Analysis and Applications 21 Probability Theory and Related Fields 19 Stochastics 19 The Annals of Probability 19 Journal of Functional Analysis 19 Proceedings of the American Mathematical Society 19 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 18 Journal of Theoretical Probability 16 Statistics & Probability Letters 15 Infinite Dimensional Analysis, Quantum Probability and Related Topics 14 The Annals of Applied Probability 13 Journal of Mathematical Analysis and Applications 13 Systems & Control Letters 11 Transactions of the American Mathematical Society 11 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 10 Journal of Soviet Mathematics 10 Acta Applicandae Mathematicae 9 Journal of Differential Equations 9 SIAM Journal on Control and Optimization 9 Electronic Journal of Probability 8 Potential Analysis 8 Stochastics and Dynamics 8 Stochastic and Partial Differential Equations. Analysis and Computations 7 Automatica 7 Information Sciences 7 Journal of Statistical Planning and Inference 7 Bernoulli 7 Stochastics 6 Computers & Mathematics with Applications 6 Mathematical and Computer Modelling 6 International Journal of Theoretical and Applied Finance 5 Journal of Mathematical Physics 5 Rocky Mountain Journal of Mathematics 5 Journal of Applied Probability 5 Journal of Optimization Theory and Applications 5 MCSS. Mathematics of Control, Signals, and Systems 5 Communications in Statistics. Theory and Methods 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Stochastics and Stochastics Reports 5 Theory of Probability and Mathematical Statistics 5 Finance and Stochastics 5 Mathematical Finance 5 Statistical Inference for Stochastic Processes 4 Advances in Applied Probability 4 Applicable Analysis 4 Biological Cybernetics 4 Journal of Statistical Physics 4 Applied Mathematics and Computation 4 Mathematische Annalen 4 Journal of Scientific Computing 4 Econometric Theory 4 Differentsial’nye Uravneniya i Protsessy Upravleniya 4 Frontiers of Mathematics in China 3 Computer Methods in Applied Mechanics and Engineering 3 Indian Journal of Pure & Applied Mathematics 3 Journal of Computational Physics 3 Journal of the Franklin Institute 3 Lithuanian Mathematical Journal 3 Physics Letters. A 3 Ukrainian Mathematical Journal 3 Arkiv för Matematik 3 Annals of the Institute of Statistical Mathematics 3 The Annals of Statistics 3 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 3 Journal of Economic Theory 3 Mathematical Systems Theory 3 Nagoya Mathematical Journal 3 Osaka Journal of Mathematics 3 Physica D 3 Acta Mathematicae Applicatae Sinica. English Series 3 Annals of Operations Research 3 Automation and Remote Control 3 Cybernetics and Systems Analysis 3 Journal of Mathematical Sciences (New York) 3 Random Operators and Stochastic Equations 3 NoDEA. Nonlinear Differential Equations and Applications 3 Electronic Communications in Probability 3 Mathematical Methods of Operations Research 3 Fractional Calculus & Applied Analysis 3 Journal of Evolution Equations 3 Discrete and Continuous Dynamical Systems. Series B 3 Central European Journal of Mathematics 3 Bulletin of the American Mathematical Society 3 Journal of Statistical Theory and Practice 3 Science China. Mathematics 3 Korean Journal of Mathematics 2 The Canadian Journal of Statistics 2 Communications in Mathematical Physics 2 Mathematical Biosciences 2 Reviews in Mathematical Physics 2 Theory of Probability and its Applications 2 Advances in Mathematics 2 Annales de l’Institut Fourier 2 Czechoslovak Mathematical Journal 2 Journal of Computational and Applied Mathematics 2 Journal of Econometrics 2 Journal of the London Mathematical Society. Second Series ...and 151 more Serials all top 5 Cited in 41 Fields 749 Probability theory and stochastic processes (60-XX) 166 Systems theory; control (93-XX) 147 Statistics (62-XX) 118 Partial differential equations (35-XX) 99 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 62 Numerical analysis (65-XX) 59 Measure and integration (28-XX) 54 Functional analysis (46-XX) 35 Quantum theory (81-XX) 30 Operator theory (47-XX) 26 Calculus of variations and optimal control; optimization (49-XX) 24 Biology and other natural sciences (92-XX) 22 Fluid mechanics (76-XX) 20 Ordinary differential equations (34-XX) 20 Dynamical systems and ergodic theory (37-XX) 15 Statistical mechanics, structure of matter (82-XX) 13 Real functions (26-XX) 13 Operations research, mathematical programming (90-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Computer science (68-XX) 8 History and biography (01-XX) 7 Information and communication theory, circuits (94-XX) 5 Potential theory (31-XX) 5 Abstract harmonic analysis (43-XX) 5 Integral equations (45-XX) 4 Nonassociative rings and algebras (17-XX) 4 Mechanics of particles and systems (70-XX) 4 Mechanics of deformable solids (74-XX) 3 Special functions (33-XX) 3 Approximations and expansions (41-XX) 3 Integral transforms, operational calculus (44-XX) 3 Geophysics (86-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Optics, electromagnetic theory (78-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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