Krylov, N. V. Some properties of solutions of Itô equations with drift in \(L_{d+1}\). (English) Zbl 1494.60065 Stochastic Processes Appl. 147, 363-387 (2022). Reviewer: Longjie Xie (Xuzhou) MSC: 60H10 60J60 PDFBibTeX XMLCite \textit{N. V. Krylov}, Stochastic Processes Appl. 147, 363--387 (2022; Zbl 1494.60065) Full Text: DOI arXiv
Krylov, N. V. On singularity as a function of time of a conditional distribution of an exit time. (English) Zbl 1344.60077 Probab. Theory Relat. Fields 165, No. 3-4, 541-557 (2016). MSC: 60J65 60H15 60J60 60G35 93E11 PDFBibTeX XMLCite \textit{N. V. Krylov}, Probab. Theory Relat. Fields 165, No. 3--4, 541--557 (2016; Zbl 1344.60077) Full Text: DOI arXiv
Krylov, N. V. Approximating the value functions for stochastic differential games with the ones having bounded second derivatives. (English) Zbl 1302.49053 Stochastic Processes Appl. 125, No. 1, 254-271 (2015). MSC: 49N70 91A15 91A23 49L25 35D40 PDFBibTeX XMLCite \textit{N. V. Krylov}, Stochastic Processes Appl. 125, No. 1, 254--271 (2015; Zbl 1302.49053) Full Text: DOI arXiv
Krylov, N. V. On regularity properties and approximations of value functions for stochastic differential games in domains. (English) Zbl 1336.91020 Ann. Probab. 42, No. 5, 2161-2196 (2014). Reviewer: Vivek S. Borkar (Mumbai) MSC: 91A23 91A15 91A05 35J60 49N70 93E20 PDFBibTeX XMLCite \textit{N. V. Krylov}, Ann. Probab. 42, No. 5, 2161--2196 (2014; Zbl 1336.91020) Full Text: DOI arXiv Euclid
Krylov, N. V. On the independence of the value function for stochastic differential games of the probability space. (English) Zbl 1307.91033 Stochastic Processes Appl. 124, No. 12, 4224-4243 (2014). MSC: 91A23 91A15 49N70 49L25 60H30 PDFBibTeX XMLCite \textit{N. V. Krylov}, Stochastic Processes Appl. 124, No. 12, 4224--4243 (2014; Zbl 1307.91033) Full Text: DOI arXiv
Krylov, N. V. On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains. (English) Zbl 1287.49027 Stochastic Processes Appl. 123, No. 8, 3273-3298 (2013). MSC: 49L20 49N70 91A15 91A23 93E20 PDFBibTeX XMLCite \textit{N. V. Krylov}, Stochastic Processes Appl. 123, No. 8, 3273--3298 (2013; Zbl 1287.49027) Full Text: DOI arXiv
Krylov, N. V. On more square root law for Brownian motion and its application to SPDEs. (English) Zbl 1048.60031 Probab. Theory Relat. Fields 127, No. 4, 496-512 (2003). Reviewer: Dominique Lepingle (Orléans) MSC: 60G17 35K05 60H15 PDFBibTeX XMLCite \textit{N. V. Krylov}, Probab. Theory Relat. Fields 127, No. 4, 496--512 (2003; Zbl 1048.60031) Full Text: DOI
Gyöngy, István; Krylov, Nicolai On the rate of convergence of splitting-up approximations for SPDEs. (English) Zbl 1038.60057 Giné, Evariste (ed.) et al., Stochastic inequalities and applications. Selected papers presented at the Euroconference on “Stochastic inequalities and their applications”, Barcelona, June 18–22, 2002. Basel: Birkhäuser (ISBN 3-7643-2197-0/hbk). Prog. Probab. 56, 301-321 (2003). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H15 65M12 60H35 65M15 65C30 35R60 93E11 93E25 PDFBibTeX XMLCite \textit{I. Gyöngy} and \textit{N. Krylov}, Prog. Probab. 56, 301--321 (2003; Zbl 1038.60057)
Krylov, N. V. Brownian trajectory is a regular lateral boundary for the heat equation. (English) Zbl 1028.60039 SIAM J. Math. Anal. 34, No. 5, 1167-1182 (2003). Reviewer: Gheorghe Oprişan (Bucureşti) MSC: 60G17 35K05 60H15 PDFBibTeX XMLCite \textit{N. V. Krylov}, SIAM J. Math. Anal. 34, No. 5, 1167--1182 (2003; Zbl 1028.60039) Full Text: DOI
Gyöngy, István; Krylov, Nicolai On the splitting-up method and stochastic partial differential equations. (English) Zbl 1028.60058 Ann. Probab. 31, No. 2, 564-591 (2003). Reviewer: Evelyn Buckwar (Berlin) MSC: 60H15 60H35 65C30 35R60 93E25 65M12 65M15 93E11 PDFBibTeX XMLCite \textit{I. Gyöngy} and \textit{N. Krylov}, Ann. Probab. 31, No. 2, 564--591 (2003; Zbl 1028.60058) Full Text: DOI
Krylov, N. V.; Zatezalo, A. A direct approach to deriving filtering equations for diffusion processes. (English) Zbl 0974.60021 Appl. Math. Optimization 42, No. 3, 315-332 (2000). Reviewer: Gabriel V.Orman (Braşov) MSC: 60G35 60H15 62M20 PDFBibTeX XMLCite \textit{N. V. Krylov} and \textit{A. Zatezalo}, Appl. Math. Optim. 42, No. 3, 315--332 (2000; Zbl 0974.60021) Full Text: DOI Link
Krylov, N. V. On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients. (English) Zbl 0971.65081 Probab. Theory Relat. Fields 117, No. 1, 1-16 (2000). Reviewer: Carlos A.De Moura (Niteroi) MSC: 65M12 35B37 93E20 49J20 93C20 65M06 PDFBibTeX XMLCite \textit{N. V. Krylov}, Probab. Theory Relat. Fields 117, No. 1, 1--16 (2000; Zbl 0971.65081) Full Text: DOI
Krylov, N. V. On Kolmogorov’s equations for finite dimensional diffusions. (English) Zbl 0943.60070 Krylov, N. V. et al., Stochastic PDE’s and Kolmogorov equations in infinite dimensions. Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo (CIME) held in Cetraro, Italy, August 24 - September 1, 1998. Berlin: Springer. Lect. Notes Math. 1715, 1-63 (1999). Reviewer: Markus Reiß (Berlin) MSC: 60J60 60H10 PDFBibTeX XMLCite \textit{N. V. Krylov}, Lect. Notes Math. 1715, 1--63 (1999; Zbl 0943.60070)
Krylov, N. V. Weighted Sobolev spaces and Laplace’s equation and the heat equations in a half space. (English) Zbl 0934.35032 Commun. Partial Differ. Equations 24, No. 9-10, 1611-1653 (1999). Reviewer: Lubomira Softova (Bari) MSC: 35J05 46E35 35K15 PDFBibTeX XMLCite \textit{N. V. Krylov}, Commun. Partial Differ. Equations 24, No. 9--10, 1611--1653 (1999; Zbl 0934.35032) Full Text: DOI
Krylov, N. V. An analytic approach to SPDEs. (English) Zbl 0933.60073 Carmona, Rene A. (ed.) et al., Stochastic partial differential equations: six perspectives. Providence, RI: American Mathematical Society. Math. Surv. Monogr. 64, 185-242 (1999). Reviewer: R.Buckdahn (Brest) MSC: 60H15 PDFBibTeX XMLCite \textit{N. V. Krylov}, Math. Surv. Monogr. 64, 185--242 (1999; Zbl 0933.60073)
Krylov, N. V. On a result of C. Mueller and E. Perkins. (English) Zbl 0886.60061 Probab. Theory Relat. Fields 108, No. 4, 543-557 (1997). Reviewer: A.D.Borisenko (Kyïv) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{N. V. Krylov}, Probab. Theory Relat. Fields 108, No. 4, 543--557 (1997; Zbl 0886.60061) Full Text: DOI
Gyöngy, István; Krylov, Nicolai Existence of strong solutions for Itô’s stochastic equations via approximations. (English) Zbl 0847.60038 Probab. Theory Relat. Fields 105, No. 2, 143-158 (1996). MSC: 60H10 PDFBibTeX XMLCite \textit{I. Gyöngy} and \textit{N. Krylov}, Probab. Theory Relat. Fields 105, No. 2, 143--158 (1996; Zbl 0847.60038) Full Text: DOI
Gyöngy, István; Krylov, Nicolai V. Stochastic partial differential equations with unbounded coefficients and applications. III. (English) Zbl 0791.60045 Stochastics Stochastics Rep. 40, No. 1-2, 77-115 (1992). Reviewer: W.Grecksch (Halle) MSC: 60H15 60G35 PDFBibTeX XMLCite \textit{I. Gyöngy} and \textit{N. V. Krylov}, Stochastics Stochastics Rep. 40, No. 1--2, 77--115 (1992; Zbl 0791.60045) Full Text: DOI
Gyöngy, I.; Krylov, N. V. On stochastic partial differential equations with unbounded coefficients. (English) Zbl 0797.60049 Da Prato, G. (ed.) et al., Stochastic partial differential equations and applications. Proceedings of the third meeting on stochastic partial differential equations and applications held at Villa Madruzzo, Trento, Italy, January 1990. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 268, 191-203 (1992). MSC: 60H15 PDFBibTeX XMLCite \textit{I. Gyöngy} and \textit{N. V. Krylov}, Pitman Res. Notes Math. Ser. 268, 191--203 (1992; Zbl 0797.60049)
Krylov, N. V. A simple proof of the existence of a solution of Itô’s equation with monotone coefficients. (English. Russian original) Zbl 0735.60061 Theory Probab. Appl. 35, No. 3, 583-587 (1990); translation from Teor. Veroyatn. Primen. 35, No. 3, 576-580 (1990). MSC: 60H10 PDFBibTeX XMLCite \textit{N. V. Krylov}, Theory Probab. Appl. 35, No. 3, 583--587 (1990; Zbl 0735.60061); translation from Teor. Veroyatn. Primen. 35, No. 3, 576--580 (1990) Full Text: DOI
Krylov, N. V. A simple proof of existence of a solution of Ito’s equation with monotone coefficients. (Russian) Zbl 0712.60062 Teor. Veroyatn. Primen. 35, No. 3, 576-580 (1990). Reviewer: C.Vârsan MSC: 60H10 PDFBibTeX XMLCite \textit{N. V. Krylov}, Teor. Veroyatn. Primen. 35, No. 3, 576--580 (1990; Zbl 0712.60062)
Krylov, N. V. On control of diffusion processes on a surface in Euclidean space. (English. Russian original) Zbl 0678.93068 Math. USSR, Sb. 65, No. 1, 185-203 (1990); translation from Mat. Sb., Nov. Ser. 137(179), No. 2(10), 184-201 (1988). MSC: 93E20 58J65 60J60 49L20 PDFBibTeX XMLCite \textit{N. V. Krylov}, Math. USSR, Sb. 65, No. 1, 185--203 (1990; Zbl 0678.93068); translation from Mat. Sb., Nov. Ser. 137(179), No. 2(10), 184--201 (1988) Full Text: DOI
Krylov, N. V. On the control of diffusion processes on a surface in Euclidean space. (Russian) Zbl 0655.93078 Mat. Sb., N. Ser. 137(179), No. 2(10), 184-201 (1988). Reviewer: Sv.Gaidov MSC: 93E20 58J65 60J60 49L20 PDFBibTeX XMLCite \textit{N. V. Krylov}, Mat. Sb., Nov. Ser. 137(179), No. 2(10), 184--201 (1988; Zbl 0655.93078) Full Text: EuDML
Krylov, N. V.; Nosovskij, G. V.; Safonov, M. V. Degeneracy domain of a nonlinearity in the Hamilton-Jacobi-Bellmann equation with constant coefficients. (English. Russian original) Zbl 0668.49020 Math. Notes 42, No. 5, 877-880 (1987); translation from Mat. Zametki 42, No. 5, 685-690 (1987). MSC: 49L20 35J60 93E20 PDFBibTeX XMLCite \textit{N. V. Krylov} et al., Math. Notes 42, No. 5, 877--880 (1987; Zbl 0668.49020); translation from Mat. Zametki 42, No. 5, 685--690 (1987) Full Text: DOI
Krylov, N. V.; Nosovskij, G. V.; Safonov, M. V. On the domain of degeneration of the nonlinearity in the Hamilton-Jacobi- Bellman equation with constant coefficients. (Russian) Zbl 0636.49010 Mat. Zametki 42, No. 5, 685-690 (1987). Reviewer: D.Jaruskova MSC: 49L20 35J60 93E20 PDFBibTeX XMLCite \textit{N. V. Krylov} et al., Mat. Zametki 42, No. 5, 685--690 (1987; Zbl 0636.49010)
Krylov, N. V.; Rozovskij, B. L. Stochastic partial differential equations and diffusion processes. (English) Zbl 0518.60072 Russ. Math. Surv. 37, No. 6, 81-105 (1982). MSC: 60H15 60G35 93E11 60H10 60J60 PDFBibTeX XMLCite \textit{N. V. Krylov} and \textit{B. L. Rozovskij}, Russ. Math. Surv. 37, No. 6, 81--105 (1982; Zbl 0518.60072) Full Text: DOI
Krylov, N. V.; Rozovskij, B. L. Stochastic partial differential equations and diffusion processes. (Russian) Zbl 0508.60054 Usp. Mat. Nauk 37, No. 6(228), 75-95 (1982). MSC: 60H15 60H10 93E11 60J60 60G35 PDFBibTeX XMLCite \textit{N. V. Krylov} and \textit{B. L. Rozovskij}, Usp. Mat. Nauk 37, No. 6(228), 75--95 (1982; Zbl 0508.60054)
Krylov, N. V.; Rozovskii, B. L. On the first integrals and Liouville equations for diffusion processes. (English) Zbl 0474.60049 Stochastic differential systems, Proc. 3rd IFIP-WG 7/1 Work. Conf., Visegrad/Hung. 1980, Lect. Notes Contr. Inf. Sci. 36, 117-125 (1981). MSC: 60H15 60J60 PDFBibTeX XML
Krylov, N. V.; Pragarauskas, G. Bellman’s equation for uniformly nondegenerate stochastic processes. (English) Zbl 0447.60043 Lith. Math. J. 20, 33-41 (1980). MSC: 60H10 93E20 60J80 45J05 PDFBibTeX XMLCite \textit{N. V. Krylov} and \textit{G. Pragarauskas}, Lith. Math. J. 20, 33--41 (1980; Zbl 0447.60043) Full Text: DOI
Krylov, N. V.; Rozovskii, B. L. On conditional distributions of diffusion processes. (English) Zbl 0402.60077 Math. USSR, Izv. 12, 336-356 (1978). MSC: 60J60 60H15 60G35 PDFBibTeX XMLCite \textit{N. V. Krylov} and \textit{B. L. Rozovskii}, Math. USSR, Izv. 12, 336--356 (1978; Zbl 0402.60077) Full Text: DOI