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Kallianpur, Gopinath (b. 1925 d. 2015)

Author ID: kallianpur.gopinath Recent zbMATH articles by "Kallianpur, Gopinath"
Published as: Kallianpur, Gopinath; Kallianpur, G.
External Links: MGP · Wikidata · Math-Net.Ru · dblp · GND · IdRef
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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

Publications by Year

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 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

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