Liu, Kai Stochastic stability of differential equations in abstract spaces. (English) Zbl 1429.35004 London Mathematical Society Lecture Note Series 453. Cambridge: Cambridge University Press (ISBN 978-1-108-70517-2/pbk; 978-1-108-65303-9/ebook). ix, 266 p. (2019). Reviewer: Aleksandr D. Borisenko (Kyïv) MSC: 35-02 60-02 35R60 60H15 35K90 35B35 47D06 35K57 PDF BibTeX XML Cite \textit{K. Liu}, Stochastic stability of differential equations in abstract spaces. Cambridge: Cambridge University Press (2019; Zbl 1429.35004) Full Text: DOI
Su, Xiaoyan; Li, Miao The regularity of fractional stochastic evolution equations in Hilbert space. (English) Zbl 1414.60049 Stochastic Anal. Appl. 36, No. 4, 639-653 (2018). MSC: 60H15 26A33 34F05 34G10 35R11 PDF BibTeX XML Cite \textit{X. Su} and \textit{M. Li}, Stochastic Anal. Appl. 36, No. 4, 639--653 (2018; Zbl 1414.60049) Full Text: DOI
Fabbri, Giorgio; Russo, Francesco HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition. (English) Zbl 1383.35234 SIAM J. Control Optim. 55, No. 6, 4072-4091 (2017). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q93 35R60 49J20 93E20 PDF BibTeX XML Cite \textit{G. Fabbri} and \textit{F. Russo}, SIAM J. Control Optim. 55, No. 6, 4072--4091 (2017; Zbl 1383.35234) Full Text: DOI
Ahmed, N. U. Systems governed by mean-field stochastic evolution equations on Hilbert spaces and their optimal control. (English) Zbl 1350.49018 Dyn. Syst. Appl. 25, No. 1-2, 61-88 (2016). MSC: 49J55 49K45 60H15 93E20 49J27 49K27 PDF BibTeX XML Cite \textit{N. U. Ahmed}, Dyn. Syst. Appl. 25, No. 1--2, 61--88 (2016; Zbl 1350.49018)
Radchenko, V. M. Evolution equations driven by general stochastic measures in Hilbert space. (English. Russian original) Zbl 1315.60004 Theory Probab. Appl. 59, No. 2, 328-339 (2015); translation from Teor. Veroyatn. Primen. 59, No. 2, 375-386 (2014). MSC: 60B11 60H05 47D06 PDF BibTeX XML Cite \textit{V. M. Radchenko}, Theory Probab. Appl. 59, No. 2, 328--339 (2015; Zbl 1315.60004); translation from Teor. Veroyatn. Primen. 59, No. 2, 375--386 (2014) Full Text: DOI
Muthukumar, P.; Rajivganthi, C. Approximate controllability of fractional order stochastic variational inequalities driven by Poisson jumps. (English) Zbl 1357.34102 Taiwanese J. Math. 18, No. 6, 1721-1738 (2014). MSC: 34G25 34A08 34K37 58E35 PDF BibTeX XML Cite \textit{P. Muthukumar} and \textit{C. Rajivganthi}, Taiwanese J. Math. 18, No. 6, 1721--1738 (2014; Zbl 1357.34102) Full Text: DOI
Ahmed, N. U. Stochastic evolution equations on Hilbert spaces with partially observed relaxed controls and their necessary conditions of optimality. (English) Zbl 1332.49030 Discuss. Math., Differ. Incl. Control Optim. 34, No. 1, 105-129 (2014). MSC: 49K45 49J55 49K27 49J27 60H15 93E20 PDF BibTeX XML Cite \textit{N. U. Ahmed}, Discuss. Math., Differ. Incl. Control Optim. 34, No. 1, 105--129 (2014; Zbl 1332.49030) Full Text: DOI
Fabbri, Giorgio; Federico, Salvatore On the infinite-dimensional representation of stochastic controlled systems with delayed control in the diffusion term. (English) Zbl 1327.39009 Math. Econ. Lett. 2, No. 3-4, 33-43 (2014). MSC: 39A50 34K30 47D06 60H99 49L20 91G20 PDF BibTeX XML Cite \textit{G. Fabbri} and \textit{S. Federico}, Math. Econ. Lett. 2, No. 3--4, 33--43 (2014; Zbl 1327.39009) Full Text: DOI
Ahmed, N. U. Stochastic neutral evolution equations on Hilbert spaces with partially observed relaxed control and their necessary conditions of optimality. (English) Zbl 1285.49017 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 101, 66-79 (2014). MSC: 49K45 49K27 93E20 60H15 PDF BibTeX XML Cite \textit{N. U. Ahmed}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 101, 66--79 (2014; Zbl 1285.49017) Full Text: DOI
Abreu, Jamil; Haak, Bernhard; van Neerven, Jan The stochastic Weiss conjecture for bounded analytic semigroups. (English) Zbl 1270.93035 J. Lond. Math. Soc., II. Ser. 88, No. 1, 181-201 (2013). MSC: 93B28 35R15 46B09 47B10 47D06 PDF BibTeX XML Cite \textit{J. Abreu} et al., J. Lond. Math. Soc., II. Ser. 88, No. 1, 181--201 (2013; Zbl 1270.93035) Full Text: DOI arXiv
Ungureanu, Viorica Mariela Stochastic uniform observability of general linear differential equations. (English) Zbl 1155.93017 Dyn. Syst. 23, No. 3, 333-350 (2008). Reviewer: Jozef Myjak (L’Aquila) MSC: 93B07 34F05 34G20 60H10 PDF BibTeX XML Cite \textit{V. M. Ungureanu}, Dyn. Syst. 23, No. 3, 333--350 (2008; Zbl 1155.93017) Full Text: DOI
Chow, Pao-Liu Stochastic partial differential equations. (English) Zbl 1134.60043 Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series. Boca Raton, FL: Chapman & Hall/CRC (ISBN 978-1-58488-443-9/hbk). ix, 281 p. (2007). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H15 60-02 35R60 PDF BibTeX XML Cite \textit{P.-L. Chow}, Stochastic partial differential equations. Boca Raton, FL: Chapman \& Hall/CRC (2007; Zbl 1134.60043)
Govindan, T. E. Asymptotic stability of mild solutions of stochastic evolution equations. (English) Zbl 1115.93093 Commun. Appl. Anal. 10, No. 2-3, 343-358 (2006). MSC: 93E15 60H20 34K50 PDF BibTeX XML Cite \textit{T. E. Govindan}, Commun. Appl. Anal. 10, No. 2--3, 343--358 (2006; Zbl 1115.93093)
Simã, Isabel A continuous kernel for the transition semigroup associated with a diffusion process in a Hilbert space. (English) Zbl 1092.47038 Semigroup Forum 71, No. 1, 49-72 (2005). Reviewer: Heinrich Hering (Rockenberg) MSC: 47D07 60J60 34K30 34G25 PDF BibTeX XML Cite \textit{I. Simã}, Semigroup Forum 71, No. 1, 49--72 (2005; Zbl 1092.47038) Full Text: DOI
Keck, David N.; McKibben, Mark A. Functional integro-differential stochastic evolution equations in Hilbert space. (English) Zbl 1031.60061 J. Appl. Math. Stochastic Anal. 16, No. 2, 141-161 (2003). Reviewer: Henri Schurz (Carbondale) MSC: 60H25 34F05 37H10 37L55 60B05 60H15 60H20 60H30 60H10 34K30 PDF BibTeX XML Cite \textit{D. N. Keck} and \textit{M. A. McKibben}, J. Appl. Math. Stochastic Anal. 16, No. 2, 141--161 (2003; Zbl 1031.60061) Full Text: DOI EuDML
Fuhrman, Marco Logarithmic derivatives of invariant measure for stochastic differential equations in Hilbert spaces. (English) Zbl 0981.60060 Stochastics Stochastics Rep. 71, No. 3-4, 269-290 (2001). Reviewer: Yu.S.Mishura (Kyïv) MSC: 60H10 60H07 60H15 60H30 PDF BibTeX XML Cite \textit{M. Fuhrman}, Stochastics Stochastics Rep. 71, No. 3--4, 269--290 (2001; Zbl 0981.60060) Full Text: DOI
Da Prato, G. Dirichlet operators for dissipative gradient systems. (English) Zbl 0976.60058 Lumer, Günter (ed.) et al., Evolution equations and their applications in physical and life sciences. Proceeding of the Bad Herrenalb (Karlsruhe) conference, Germany, 1999. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 215, 483-492 (2001). Reviewer: Mihai Gradinaru (Nancy) MSC: 60H15 47D06 PDF BibTeX XML Cite \textit{G. Da Prato}, Lect. Notes Pure Appl. Math. 215, 483--492 (2001; Zbl 0976.60058)
Liu, Kai; Zou, Jiezhong Lyapunov function approach and stochastic stability in infinite-dimensional spaces. (English) Zbl 1030.93047 Adv. Math., Beijing 29, No. 5, 385-396 (2000). Reviewer: M.Nisio (Osaka) MSC: 93E15 93C25 60H10 93D05 PDF BibTeX XML Cite \textit{K. Liu} and \textit{J. Zou}, Adv. Math., Beijing 29, No. 5, 385--396 (2000; Zbl 1030.93047)
Spectorsky, I. Stochastic equations in the space of formal series: Convergence of solution series. (English) Zbl 0949.60073 Adamyan, V. M. (ed.) et al., Operator theory and related topics. Proceedings of the Mark Krein international conference on operator theory and applications, Odessa, Ukraine, August 18-22, 1997. Volume II. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 118, 373-387 (2000). MSC: 60H10 58D25 PDF BibTeX XML Cite \textit{I. Spectorsky}, in: Operator theory and related topics. Proceedings of the Mark Krein international conference on operator theory and applications, Odessa, Ukraine, August 18--22, 1997. Volume II. Basel: Birkhäuser. 373--387 (2000; Zbl 0949.60073)
Zabczyk, J. On asymptotic properties of infinite dimensional stochastic systems. (English) Zbl 1040.35161 CWI Q. 12, No. 3-4, 369-376 (1999). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35R60 60J60 35R15 60H15 PDF BibTeX XML Cite \textit{J. Zabczyk}, CWI Q. 12, No. 3--4, 369--376 (1999; Zbl 1040.35161)
Barchielli, A.; Paganoni, A. M.; Zucca, F. On stochastic differential equations and semigroups of probability operators in quantum probability. (English) Zbl 0940.60078 Stochastic Processes Appl. 73, No. 1, 69-86 (1998). Reviewer: B.Maslowski (Praha) MSC: 60H10 47D06 58D25 PDF BibTeX XML Cite \textit{A. Barchielli} et al., Stochastic Processes Appl. 73, No. 1, 69--86 (1998; Zbl 0940.60078) Full Text: DOI
Pohl, Thomas; Grecksch, Wilfried; Blaar, Holger A parallel modified Lagrangian method for an optimal control problem of a linear distributed stochastic system. (English) Zbl 0923.65038 Monte Carlo Methods Appl. 4, No. 4, 319-340 (1998). Reviewer: Lubomír Bakule (Praha) MSC: 65K10 60H15 49K27 49M29 65Y05 PDF BibTeX XML Cite \textit{T. Pohl} et al., Monte Carlo Methods Appl. 4, No. 4, 319--340 (1998; Zbl 0923.65038) Full Text: DOI
Flandoli, Franco Stochastic evolution equations with non-coercive monotone operators. (English) Zbl 0846.34087 Lakshmikantham, V. (ed.), World congress of nonlinear analysts ’92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 1765-1777 (1996). MSC: 34K50 34G20 34F05 47J05 PDF BibTeX XML Cite \textit{F. Flandoli}, in: World congress of nonlinear analysts '92. Proceedings of the first world congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter. 1765--1777 (1996; Zbl 0846.34087)
Twardowska, Krystyna An approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations. (English) Zbl 0839.60059 Stochastic Anal. Appl. 13, No. 5, 601-626 (1995). MSC: 60H15 60F15 PDF BibTeX XML Cite \textit{K. Twardowska}, Stochastic Anal. Appl. 13, No. 5, 601--626 (1995; Zbl 0839.60059) Full Text: DOI
Fuhrman, M. A note on the nonsymmetric Ornstein-Uhlenbeck process in Hilbert spaces. (English) Zbl 0821.60048 Appl. Math. Lett. 8, No. 3, 19-22 (1995). MSC: 60G15 60H10 PDF BibTeX XML Cite \textit{M. Fuhrman}, Appl. Math. Lett. 8, No. 3, 19--22 (1995; Zbl 0821.60048) Full Text: DOI
Gątarek, Dariusz Existence of optimal controls for stochastic evolution systems. (English) Zbl 0821.60068 DaPrato, Giuseppe (ed.) et al., Control of partial differential equations. IFIP WG 7.2 Conference, Villa Madruzzo, Trento, Italy, January 4-9, 1993. New York, NY: Marcel Dekker, Inc. Lect. Notes Pure Appl. Math. 165, 81-86 (1994). Reviewer: W.Grecksch (Halle) MSC: 60H15 49J55 49J27 49J20 PDF BibTeX XML Cite \textit{D. Gątarek}, Lect. Notes Pure Appl. Math. 165, 81--86 (1994; Zbl 0821.60068)
Xu, Minghao Some properties of the solution of semilinear stochastic evolution equations in Hilbert spaces. (Chinese. English summary) Zbl 0805.60054 J. Wuhan Univ., Nat. Sci. Ed. 1994, No. 2, 29-36 (1994). Reviewer: Wu Chengxun (Shanghai) MSC: 60H15 60H10 PDF BibTeX XML Cite \textit{M. Xu}, J. Wuhan Univ., Nat. Sci. Ed. 1994, No. 2, 29--36 (1994; Zbl 0805.60054)
Vrkoč, Ivo A dynamical system in a Hilbert space with a weakly attractive nonstationary point. (English) Zbl 0794.34054 Math. Bohem. 118, No. 4, 401-423 (1993). Reviewer: R.Manthey (Jena) MSC: 34G20 34F05 60H15 PDF BibTeX XML Cite \textit{I. Vrkoč}, Math. Bohem. 118, No. 4, 401--423 (1993; Zbl 0794.34054) Full Text: EuDML
Gątarek, Dariusz A note on nonlinear stochastic equations in Hilbert spaces. (English) Zbl 0786.60089 Stat. Probab. Lett. 17, No. 5, 387-394 (1993). Reviewer: J.Jakubowski (Warszawa) MSC: 60H25 PDF BibTeX XML Cite \textit{D. Gątarek}, Stat. Probab. Lett. 17, No. 5, 387--394 (1993; Zbl 0786.60089) Full Text: DOI
Twardowska, Krystyna Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions. (English) Zbl 0777.60051 Diss. Math. 325, 54 p. (1993). Reviewer: Nguyêñ Hôǹg Thái (Minsk) MSC: 60H10 34K50 60H05 60H15 60H30 35G20 35K50 35R15 PDF BibTeX XML Cite \textit{K. Twardowska}, Diss. Math. 325, 54 p. (1993; Zbl 0777.60051)
Ahmed, N. U. Semilinear and quasilinear stochastic differential equations in Banach spaces. (English) Zbl 0832.34051 Agarwal, R. P. (ed.), Recent trends in differential equations. Singapore: World Scientific Publishing. World Sci. Ser. Appl. Anal. 1, 1-14 (1992). MSC: 34G20 34F05 PDF BibTeX XML Cite \textit{N. U. Ahmed}, in: Recent trends in differential equations. Singapore: World Scientific Publishing. 1--14 (1992; Zbl 0832.34051)
Goldys, Beniamin On weak solutions of stochastic evolution equations with unbounded coefficients. (English) Zbl 0798.60063 Doust, Ian (ed.) et al., Proceedings of the miniconference on probability and analysis, held at the University of New South Wales, Sydney, Australia, July 24-26, 1991. Canberra: Centre for Mathematics and Its Applications, Australian National University. Proc. Cent. Math. Appl. Aust. Natl. Univ. 29, 116-128 (1991). Reviewer: F.Flandoli (Pisa) MSC: 60H15 35R60 34G20 PDF BibTeX XML Cite \textit{B. Goldys}, Proc. Cent. Math. Appl. Aust. Natl. Univ. 29, 116--128 (1991; Zbl 0798.60063)
Daletskij, Yu. L.; Fomin, S. V. Measures and differential equations in infinite-dimensional space. (English) Zbl 0753.46027 Mathematics and Its Applications. Soviet Series. 76. Dordrecht etc.: Kluwer Academic Publishers. xv, 337 p. (1991). Reviewer: W.Slowikowski (Aarhus) MSC: 46G12 28C20 46-02 28-02 46G05 46F25 PDF BibTeX XML Cite \textit{Yu. L. Daletskij} and \textit{S. V. Fomin}, Measures and differential equations in infinite-dimensional space. Dordrecht etc.: Kluwer Academic Publishers (1991; Zbl 0753.46027)
Serrano, Sergio E.; Unny, T. E. Random evolution equations in hydrology. (English) Zbl 0706.76107 Appl. Math. Comput. 39, No. 3, Suppl., 97s-122s (1990). MSC: 76S05 76A05 35R60 60H15 PDF BibTeX XML Cite \textit{S. E. Serrano} and \textit{T. E. Unny}, Appl. Math. Comput. 39, No. 3, 97s-122s (1990; Zbl 0706.76107) Full Text: DOI
Serrano, Sergio E.; Unny, T. E. Random evolution equations in hydrology. (English) Zbl 0699.76110 Appl. Math. Comput. 38, No. 3, 201-226 (1990). MSC: 76S05 60H15 35R60 PDF BibTeX XML Cite \textit{S. E. Serrano} and \textit{T. E. Unny}, Appl. Math. Comput. 38, No. 3, 201--226 (1990; Zbl 0699.76110) Full Text: DOI
Butsan, G. P. A mixed product of dependent stochastic operator systems. (English. Russian original) Zbl 0783.47058 Sov. Math., Dokl. 40, No. 1, 229-234 (1990); translation from Dokl. Akad. Nauk SSSR 307, No. 6, 1300-1304 (1989). Reviewer: W.Hazod (Dortmund) MSC: 47D07 47L30 47D06 60B99 PDF BibTeX XML Cite \textit{G. P. Butsan}, Sov. Math., Dokl. 40, No. 1, 229--234 (1989; Zbl 0783.47058); translation from Dokl. Akad. Nauk SSSR 307, No. 6, 1300--1304 (1989)
Tudor, Constantin Quadratic control for linear stochastic evolution equations. (English) Zbl 0654.93080 Stud. Cercet. Mat. 40, No. 3, 259-276 (1988). Reviewer: Sv.Gaidov MSC: 93E20 49J55 93C25 93C05 45N05 PDF BibTeX XML Cite \textit{C. Tudor}, Stud. Cercet. Mat. 40, No. 3, 259--276 (1988; Zbl 0654.93080)
Ichikawa, Akira Bounded solutions and periodic solutions of a linear stochastic evolution equation. (English) Zbl 0633.60084 Probability theory and mathematical statistics, Proc. 5th Jap.-USSR Symp., Kyoto/Jap. 1986, Lect. Notes Math. 1299, 124-130 (1988). MSC: 60H25 93E15 93C25 PDF BibTeX XML
Dawson, D. A.; Gorostiza, L. G. *-solutions of evolution equations in Hilbert space. (English) Zbl 0613.34048 J. Differ. Equations 68, 299-319 (1987). Reviewer: H.Engler MSC: 34G10 34G20 47D03 PDF BibTeX XML Cite \textit{D. A. Dawson} and \textit{L. G. Gorostiza}, J. Differ. Equations 68, 299--319 (1987; Zbl 0613.34048) Full Text: DOI
Axelsson, O. On the B-convergence of the \(\theta\)-method over infinite time for time stepping for evolution equations. (English) Zbl 0614.65065 Trends in the theory and practice of nonlinear analysis, Proc. 6th Int. Conf., Arlington/Tex. 1984, North-Holland Math. Stud. 110, 33-40 (1985). Reviewer: Michael Sever (Jerusalem) MSC: 65J15 65L05 62L20 35G10 35K25 34G20 PDF BibTeX XML
Zabczyk, J. Structural properties and limit behaviour of linear stochastic systems in Hilbert spaces. (English) Zbl 0573.93076 Mathematical control theory, Banach Cent. Publ. 14, 591-609 (1985). Reviewer: R.Curtain MSC: 93E15 60J25 93C05 46C99 60H25 93C25 47D03 93B05 93E20 PDF BibTeX XML
Mel’nik, S. A. Finite-difference approximation for the solution of a stochastic evolution equation. (Russian) Zbl 0619.65149 Teor. Sluchajnykh Protsessov 12, 56-59 (1984). MSC: 65C99 65R20 65J15 60H20 45N05 PDF BibTeX XML Cite \textit{S. A. Mel'nik}, Teor. Sluch. Protsess. 12, 56--59 (1984; Zbl 0619.65149)
Loges, Wilfried Girsanov’s theorem in Hilbert space and an application to the statistics of Hilbert space-valued stochastic differential equations. (English) Zbl 0553.93059 Stochastic Processes Appl. 17, 243-263 (1984). Reviewer: R.Curtain MSC: 93E10 60H15 62F12 46C99 62A01 93C05 93C25 PDF BibTeX XML Cite \textit{W. Loges}, Stochastic Processes Appl. 17, 243--263 (1984; Zbl 0553.93059) Full Text: DOI
Ahmed, N. U. Stochastic control on Hilbert space for linear evolution equations with random operator-valued coefficients. (English) Zbl 0468.49009 SIAM J. Control Optimization 19, 401-430 (1981). MSC: 49J55 49K27 60H15 60H25 PDF BibTeX XML Cite \textit{N. U. Ahmed}, SIAM J. Control Optim. 19, 401--430 (1981; Zbl 0468.49009) Full Text: DOI
Chojnowska Michalik, Anna Representation theorem for general stochastic delay equations. (English) Zbl 0415.60057 Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 26, 635-642 (1978). MSC: 60H20 34F05 34K30 34G20 PDF BibTeX XML Cite \textit{A. Chojnowska Michalik}, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 26, 635--642 (1978; Zbl 0415.60057)