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Krylov, Nikolai Vladimirovich

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Total publications: 81
Scientific articles: 77
Presentations: 1

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Abstract pages:28962
Full texts:10716
References:1630
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Publications in Math-Net.Ru
2019
1. N. V. Krylov, “Weighted Aleksandrov estimates: PDE and stochastic versions”, Algebra i Analiz, 31:3 (2019),  154–169  mathnet
2015
2. N. V. Krylov, “Hörmander's theorem for stochastic partial differential equations”, Algebra i Analiz, 27:3 (2015),  157–182  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:3 (2016), 461–479  isi  scopus
2012
3. Hongjie Dong, N. V. Krylov, Xu Li, “On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains”, Algebra i Analiz, 24:1 (2012),  53–94  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 24:1 (2013), 39–69  isi  scopus
2009
4. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Uspekhi Mat. Nauk, 64:6(390) (2009),  5–116  mathnet  mathscinet  elib; Russian Math. Surveys, 64:6 (2009), 973–1078  isi  elib  scopus
2005
5. Hongjie Dong, N. V. Krylov, “On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients”, Algebra i Analiz, 17:2 (2005),  108–132  mathnet  mathscinet  zmath; St. Petersburg Math. J., 17:2 (2006), 295–313
2002
6. N. V. Krylov, “Parabolic equations in $L_p$-spaces with mixed norms”, Algebra i Analiz, 14:4 (2002),  91–106  mathnet  mathscinet  zmath; St. Petersburg Math. J., 14:4 (2003), 603–614
2001
7. N. V. Krylov, “On the Caiderón–Zygmund theorem with applications to parabolic equations”, Algebra i Analiz, 13:4 (2001),  1–25  mathnet  mathscinet  zmath; St. Petersburg Math. J., 13:4 (2002), 509–526
1997
8. N. V. Krylov, “On the rate of convergence of finite-difference approximations for Bellman's equations”, Algebra i Analiz, 9:3 (1997),  245–256  mathnet  mathscinet  zmath; St. Petersburg Math. J., 9:3 (1998), 639–650
1993
9. N. V. Krylov, “On a proof of Itô's formula”, Trudy Mat. Inst. Steklov., 202 (1993),  170–174  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 202 (1994), 139–142
1992
10. N. V. Krylov, “On the first quasiderivatives of solutions of Ito stochastic equations”, Izv. RAN. Ser. Mat., 56:2 (1992),  398–426  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 40:2 (1993), 377–403  isi
1990
11. N. V. Krylov, “A simple proof of the existence of a solution to the Itô equation with monotone coefficients”, Teor. Veroyatnost. i Primenen., 35:3 (1990),  576–580  mathnet  mathscinet  zmath; Theory Probab. Appl., 35:3 (1990), 583–587  isi
1989
12. N. V. Krylov, “Smoothness of the value function for a controlled diffusion process in a domain”, Izv. Akad. Nauk SSSR Ser. Mat., 53:1 (1989),  66–96  mathnet  mathscinet  zmath; Math. USSR-Izv., 34:1 (1990), 65–95
13. S. V. Anulova, A. Yu. Veretennikov, N. V. Krylov, R. Sh. Liptser, A. N. Shiryaev, “Stochastic calculus”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 45 (1989),  5–253  mathnet  mathscinet  zmath
1988
14. N. V. Krylov, “On control of diffusion processes on a surface in Euclidean space”, Mat. Sb. (N.S.), 137(179):2(10) (1988),  184–201  mathnet  mathscinet  zmath; Math. USSR-Sb., 65:1 (1990), 185–203
15. N. V. Krylov, “On moment estimates for quasiderivative of solutions of stochastic equations with respect to the initial data, and their applications”, Mat. Sb. (N.S.), 136(178):4(8) (1988),  510–529  mathnet  mathscinet  zmath; Math. USSR-Sb., 64:2 (1989), 505–526
16. N. V. Krylov, “On unconditional solvability of the Bellman equation with constant coefficients in convex domains”, Mat. Sb. (N.S.), 135(177):3 (1988),  297–311  mathnet  mathscinet  zmath; Math. USSR-Sb., 63:2 (1989), 289–303
17. L. A. Aljushina, N. V. Krylov, “On the Passage to the Limit in Ito's Stochastic Equations”, Teor. Veroyatnost. i Primenen., 33:1 (1988),  3–13  mathnet  mathscinet  zmath; Theory Probab. Appl., 33:1 (1988), 1–10  isi
1987
18. N. V. Krylov, “On the first boundary value problem for nonlinear degenerate elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 51:2 (1987),  242–269  mathnet  mathscinet  zmath; Math. USSR-Izv., 30:2 (1988), 217–244
19. N. V. Krylov, G. V. Nosovskii, M. V. Safonov, “Degeneracy domain of a nonlinearity in the Hamilton–Jacobi–Bellman equation with constant coefficients”, Mat. Zametki, 42:5 (1987),  685–690  mathnet  mathscinet  zmath; Math. Notes, 42:5 (1987), 877–880  isi
1986
20. N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Mat. Sb. (N.S.), 130(172):2(6) (1986),  207–221  mathnet  mathscinet  zmath; Math. USSR-Sb., 58:1 (1987), 207–221
21. N. V. Krylov, “An approach to controlled diffusion processes”, Teor. Veroyatnost. i Primenen., 31:4 (1986),  685–709  mathnet  mathscinet  zmath; Theory Probab. Appl., 31:4 (1987), 604–626  isi
22. N. V. Krylov, “The sufficiency of the adjointed Markov policies for the controlled diffusion processes”, Teor. Veroyatnost. i Primenen., 31:2 (1986),  353–358  mathnet  mathscinet  zmath; Theory Probab. Appl., 31:2 (1987), 304–309  isi
1985
23. N. V. Krylov, “$G$-convergence of elliptic operators in nondivergence form”, Mat. Zametki, 37:4 (1985),  522–527  mathnet  mathscinet  zmath; Math. Notes, 37:4 (1985), 290–292  isi
1984
24. N. V. Krylov, “Estimates for derivatives of the solutions of nonlinear parabolic equations”, Dokl. Akad. Nauk SSSR, 274:1 (1984),  23–26  mathnet  mathscinet  zmath
25. N. V. Krylov, “Extremal properties of the solutions of stochastic equations”, Teor. Veroyatnost. i Primenen., 29:2 (1984),  209–221  mathnet  mathscinet  zmath; Theory Probab. Appl., 29:2 (1985), 205–217  isi
1983
26. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations in a domain”, Izv. Akad. Nauk SSSR Ser. Mat., 47:1 (1983),  75–108  mathnet  mathscinet  zmath; Math. USSR-Izv., 22:1 (1984), 67–97
27. N. V. Krylov, “On degenerate nonlinear elliptic equations. II”, Mat. Sb. (N.S.), 121(163):2(6) (1983),  211–232  mathnet  mathscinet  zmath; Math. USSR-Sb., 49:1 (1984), 207–228
28. N. V. Krylov, “On degenerate nonlinear elliptic equations”, Mat. Sb. (N.S.), 120(162):3 (1983),  311–330  mathnet  mathscinet  zmath; Math. USSR-Sb., 48:2 (1984), 307–326
1982
29. N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982),  487–523  mathnet  mathscinet  zmath; Math. USSR-Izv., 20:3 (1983), 459–492
30. N. V. Krylov, B. L. Rozovskii, “Stochastic partial differential equations and diffusion processes”, Uspekhi Mat. Nauk, 37:6(228) (1982),  75–95  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:6 (1982), 81–105  isi
1981
31. N. V. Krylov, “On control of a diffusion process up to the time of first exit from a region”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981),  1029–1048  mathnet  mathscinet  zmath; Math. USSR-Izv., 19:2 (1982), 297–313
32. N. V. Krylov, “On controlled diffusion processes with unbounded coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 45:4 (1981),  734–759  mathnet  mathscinet  zmath; Math. USSR-Izv., 19:1 (1982), 41–64
1980
33. N. V. Krylov, M. V. Safonov, “A certain property of solutions of parabolic equations with measurable coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980),  161–175  mathnet  mathscinet  zmath; Math. USSR-Izv., 16:1 (1981), 151–164  isi
34. N. V. Krylov, T. P. Mirošničenko, “On extension of optimality set of Wald test”, Teor. Veroyatnost. i Primenen., 25:1 (1980),  167–171  mathnet  mathscinet  zmath; Theory Probab. Appl., 25:1 (1980), 165–169  isi
1979
35. N. V. Krylov, B. L. Rozovskii, “Ito equations in Banach spaces and strongly parabolic stochastic partial differential equations”, Dokl. Akad. Nauk SSSR, 249:2 (1979),  285–289  mathnet  mathscinet  zmath
36. N. V. Krylov, “On the theory of controlled diffusion processes”, Dokl. Akad. Nauk SSSR, 245:2 (1979),  298–300  mathnet  mathscinet  zmath
37. N. V. Krylov, M. V. Safonov, “An estimate for the probability of a diffusion process hitting a set of positive measure”, Dokl. Akad. Nauk SSSR, 245:1 (1979),  18–20  mathnet  mathscinet
38. N. V. Krylov, B. L. Rozovskii, “Stochastic evolution equations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 14 (1979),  71–146  mathnet  mathscinet  zmath; J. Soviet Math., 16:4 (1981), 1233–1277
39. N. V. Krylov, “Some new results in the theory of controlled diffusion processes”, Mat. Sb. (N.S.), 109(151):1(5) (1979),  146–164  mathnet  mathscinet  zmath; Math. USSR-Sb., 37:1 (1980), 133–149  isi
40. N. V. Krylov, “On the coincidence of $\sigma$-algebras in the filtration problem for diffusion processes”, Teor. Veroyatnost. i Primenen., 24:4 (1979),  771–780  mathnet  mathscinet  zmath; Theory Probab. Appl., 24:4 (1980), 772–781  isi
1978
41. N. V. Krylov, “On the limit passage in parabolic Bellman equations”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978),  1417–1425  mathnet  mathscinet  zmath; Math. USSR-Izv., 13:3 (1979), 677–684  isi
42. N. V. Krylov, “On the maximum principle for nonlinear parabolic and elliptic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 42:5 (1978),  1050–1062  mathnet  mathscinet  zmath; Math. USSR-Izv., 13:2 (1979), 335–347  isi
43. N. V. Krylov, B. L. Rozovskii, “On conditional distributions of diffusion processes”, Izv. Akad. Nauk SSSR Ser. Mat., 42:2 (1978),  356–378  mathnet  mathscinet  zmath; Math. USSR-Izv., 12:2 (1978), 336–356
44. N. V. Krylov, “On passing to the limit in degenerate Bellman equations. II”, Mat. Sb. (N.S.), 107(149):1(9) (1978),  56–68  mathnet  mathscinet  zmath; Math. USSR-Sb., 35:3 (1979), 351–362  isi
45. N. V. Krylov, “On passing to the limit in degenerate Bellman equations. I”, Mat. Sb. (N.S.), 106(148):2(6) (1978),  214–233  mathnet  mathscinet  zmath; Math. USSR-Sb., 34:6 (1978), 765–783
46. N. V. Krylov, “Some properties of the normal image of convex functions”, Mat. Sb. (N.S.), 105(147):2 (1978),  180–191  mathnet  mathscinet  zmath; Math. USSR-Sb., 34:2 (1978), 161–171
1977
47. N. V. Krylov, B. L. Rozovskii, “On the Cauchy problem for linear stochastic partial differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 41:6 (1977),  1329–1347  mathnet  mathscinet  zmath; Math. USSR-Izv., 11:6 (1977), 1267–1284
1976
48. N. V. Krylov, “The maximum principle for parabolic equations”, Uspekhi Mat. Nauk, 31:4(190) (1976),  267–268  mathnet  mathscinet  zmath
49. A. Yu. Veretennikov, N. V. Krylov, “On explicit formulas for solutions of stochastic equations”, Mat. Sb. (N.S.), 100(142):2(6) (1976),  266–284  mathnet  mathscinet  zmath; Math. USSR-Sb., 29:2 (1976), 239–256  isi
50. I. L. Genis, N. V. Krylov, “An example of a one-dimensional controlled process”, Teor. Veroyatnost. i Primenen., 21:1 (1976),  147–151  mathnet  mathscinet  zmath; Theory Probab. Appl., 21:1 (1976), 148–152
1974
51. N. V. Krylov, “Some estimates of the probability density of a stochastic integral”, Izv. Akad. Nauk SSSR Ser. Mat., 38:1 (1974),  228–248  mathnet  mathscinet  zmath; Math. USSR-Izv., 8:1 (1974), 233–254
1973
52. N. V. Krylov, “On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973),  691–708  mathnet  mathscinet  zmath; Math. USSR-Izv., 7:3 (1973), 691–709
53. N. V. Krylov, “О регулярности условных вероятностей для случайных процессов”, Teor. Veroyatnost. i Primenen., 18:1 (1973),  151–155  mathnet  mathscinet  zmath; Theory Probab. Appl., 18:1 (1973), 150–153
54. N. V. Krylov, “Some estimates in the theory of stochastic integral”, Teor. Veroyatnost. i Primenen., 18:1 (1973),  56–65  mathnet  mathscinet  zmath; Theory Probab. Appl., 18:1 (1973), 54–63
1972
55. N. V. Krylov, “On control of the solution of a stochastic integral equation with degeneration”, Izv. Akad. Nauk SSSR Ser. Mat., 36:1 (1972),  248–261  mathnet  mathscinet  zmath; Math. USSR-Izv., 6:1 (1972), 249–262
56. N. V. Krylov, “Control of a Solution of a Stochastic Integral Equation”, Teor. Veroyatnost. i Primenen., 17:1 (1972),  111–128  mathnet  mathscinet  zmath; Theory Probab. Appl., 17:1 (1972), 114–13
1971
57. N. V. Krylov, “On the theory of nonlinear degenerating elliptic equations”, Dokl. Akad. Nauk SSSR, 201:6 (1971),  1279–1281  mathnet  mathscinet  zmath
58. N. V. Krylov, “On uniqueness of the solution of Bellman's equation”, Izv. Akad. Nauk SSSR Ser. Mat., 35:6 (1971),  1377–1388  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:6 (1971), 1387–1398
59. N. V. Krylov, “Control of Markov processes and $W$-spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 35:1 (1971),  224–255  mathnet  mathscinet  zmath; Math. USSR-Izv., 5:1 (1971), 233–266
60. N. V. Krylov, “On an inequality in the theory of stochastic integrals”, Teor. Veroyatnost. i Primenen., 16:3 (1971),  446–457  mathnet  mathscinet  zmath; Theory Probab. Appl., 16:3 (1971), 438–448
1970
61. N. V. Krylov, “The problem with two free boundaries for an elliptic equation and the optimal stopping of a Markov process”, Dokl. Akad. Nauk SSSR, 194:6 (1970),  1263–1265  mathnet  mathscinet  zmath
62. N. V. Krylov, “Bounded inhomogeneous nonlinear elliptic and parabolic equations in the plane”, Mat. Sb. (N.S.), 82(124):1(5) (1970),  99–110  mathnet  mathscinet  zmath; Math. USSR-Sb., 11:1 (1970), 89–99
63. N. V. Krylov, “On equations of minimax type in the theory of elliptic and parabolic equations in the plane”, Mat. Sb. (N.S.), 81(123):1 (1970),  3–22  mathnet  mathscinet  zmath; Math. USSR-Sb., 10:1 (1970), 1–19
1969
64. N. V. Krylov, “Parabolic equations on the plane and semigroups”, Differ. Uravn., 5:12 (1969),  2216–2224  mathnet  mathscinet  zmath
65. N. V. Krylov, “Boundedly nonhomogeneous nonlinear elliptic and parabolic equations in the plane”, Uspekhi Mat. Nauk, 24:4(148) (1969),  201–202  mathnet  mathscinet  zmath
66. N. V. Krylov, “On a class of nonlinear equations in a space of measurable functions”, Mat. Sb. (N.S.), 80(122):2(10) (1969),  253–265  mathnet  mathscinet  zmath; Math. USSR-Sb., 9:2 (1969), 241–251
67. N. V. Krylov, “On Ito stochastic integral equations”, Teor. Veroyatnost. i Primenen., 14:2 (1969),  340–348  mathnet  mathscinet  zmath; Theory Probab. Appl., 14:2 (1969), 330–336
1967
68. N. V. Krylov, “The first boundary value problem for elliptic equations of second order”, Differ. Uravn., 3:2 (1967),  315–326  mathnet  mathscinet  zmath
69. N. V. Krylov, “On the Green's function for the Dirichlet problem”, Uspekhi Mat. Nauk, 22:2(134) (1967),  116–118  mathnet  mathscinet
1966
70. N. V. Krylov, “On solutions of elliptic equations of the second order”, Uspekhi Mat. Nauk, 21:2(128) (1966),  233–235  mathnet  mathscinet
71. N. V. Krylov, “Some properties of quasidiffusion process”, Uspekhi Mat. Nauk, 21:1(127) (1966),  177–179  mathnet
72. N. V. Krylov, “On regular boundary points for Markov processes”, Teor. Veroyatnost. i Primenen., 11:4 (1966),  690–695  mathnet  mathscinet  zmath; Theory Probab. Appl., 11:4 (1966), 609–614
73. N. V. Krylov, “On quasi-diffusional processes”, Teor. Veroyatnost. i Primenen., 11:3 (1966),  424–443  mathnet  mathscinet  zmath; Theory Probab. Appl., 11:3 (1966), 373–389
1965
74. N. V. Krylov, A. A. Yushkevich, “Markov random sets”, Tr. Mosk. Mat. Obs., 13 (1965),  114–135  mathnet  mathscinet  zmath
75. N. V. Krylov, “The Construction of an Optimal Strategy for a Finite Controlled Chain”, Teor. Veroyatnost. i Primenen., 10:1 (1965),  51–60  mathnet  mathscinet  zmath; Theory Probab. Appl., 10:1 (1965), 45–54
1964
76. N. V. Krylov, “On the existence of $\varepsilon$-optimal homogeneous Markov strategies for a controlled chain”, Dokl. Akad. Nauk SSSR, 155:4 (1964),  747–750  mathnet  mathscinet  zmath
77. N. V. Krylov, A. A. Yuškevič, “On Markov Random Sets”, Teor. Veroyatnost. i Primenen., 9:4 (1964),  738–743  mathnet  mathscinet  zmath; Theory Probab. Appl., 9:4 (1964), 666–670

1994
78. N. V. Krylov, S. E. Kuznetsov, A. V. Skorokhod, A. A. Yushkevich, “E. B. Dynkin's 70th Birthday”, Teor. Veroyatnost. i Primenen., 39:4 (1994),  796–798  mathnet  mathscinet; Theory Probab. Appl., 39:4 (1994), 654–656  isi
1980
79. N. V. Krylov, M. V. Safonov, V. P. Maslov, L. A. Bunimovich, Ya. G. Sinai, S. M. Kozlov, V. E. Zakharov, A. G. Aslanyan, D. G. Vasil'ev, V. B. Lidskii, R. I. Nigmatulin, V. M. Petkov, “Sessions of the Petrovskii Seminar on differential equations and problems of mathematical physics”, Uspekhi Mat. Nauk, 35:2(212) (1980),  251–256  mathnet
1979
80. F. John, J. Leray, S. P. Novikov, A. G. Khovanskii, S. A. Molchanov, N. V. Krylov, B. L. Rozovskii, N. R. Sibgatullin, A. V. Uglanov, S. Yu. Dobrokhotov, V. P. Maslov, “Sessions of the Petrovskii Seminar on differential equations and mathematical problems of physics”, Uspekhi Mat. Nauk, 34:3(207) (1979),  221–226  mathnet
1972
81. N. V. Krylov, “Addendum: On Ito's Stochastic Integral Equations”, Teor. Veroyatnost. i Primenen., 17:2 (1972),  392–393  mathnet  mathscinet  zmath; Theory Probab. Appl., 17:2 (1973), 373–374

Presentations in Math-Net.Ru
1. On the problem of filtering for partially observed diffusion process
N. V. Krylov
Dobrushin Mathematics Laboratory Seminar
May 31, 2011 16:00

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