Publications in Math-Net.Ru |
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2019 |
1. |
N. V. Krylov, “Weighted Aleksandrov estimates: PDE and stochastic versions”, Algebra i Analiz, 31:3 (2019), 154–169 |
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2015 |
2. |
N. V. Krylov, “Hörmander's theorem for stochastic partial differential equations”, Algebra i Analiz, 27:3 (2015), 157–182 ; St. Petersburg Math. J., 27:3 (2016), 461–479 |
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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 ; St. Petersburg Math. J., 24:1 (2013), 39–69 |
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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 ; Russian Math. Surveys, 64:6 (2009), 973–1078 |
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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 ; St. Petersburg Math. J., 17:2 (2006), 295–313 |
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2002 |
6. |
N. V. Krylov, “Parabolic equations in $L_p$-spaces with mixed norms”, Algebra i Analiz, 14:4 (2002), 91–106 ; St. Petersburg Math. J., 14:4 (2003), 603–614 |
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2001 |
7. |
N. V. Krylov, “On the Caiderón–Zygmund theorem with applications to parabolic equations”, Algebra i Analiz, 13:4 (2001), 1–25 ; St. Petersburg Math. J., 13:4 (2002), 509–526 |
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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 ; St. Petersburg Math. J., 9:3 (1998), 639–650 |
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1993 |
9. |
N. V. Krylov, “On a proof of Itô's formula”, Trudy Mat. Inst. Steklov., 202 (1993), 170–174 ; Proc. Steklov Inst. Math., 202 (1994), 139–142 |
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1992 |
10. |
N. V. Krylov, “On the first quasiderivatives of solutions of Ito stochastic equations”, Izv. RAN. Ser. Mat., 56:2 (1992), 398–426 ; Russian Acad. Sci. Izv. Math., 40:2 (1993), 377–403 |
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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 ; Theory Probab. Appl., 35:3 (1990), 583–587 |
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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 ; 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 |
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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 ; 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 ; 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 ; 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 ; Theory Probab. Appl., 33:1 (1988), 1–10 |
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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 ; 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 ; Math. Notes, 42:5 (1987), 877–880 |
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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 ; 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 ; Theory Probab. Appl., 31:4 (1987), 604–626 |
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 ; Theory Probab. Appl., 31:2 (1987), 304–309 |
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1985 |
23. |
N. V. Krylov, “$G$-convergence of elliptic operators in nondivergence form”, Mat. Zametki, 37:4 (1985), 522–527 ; Math. Notes, 37:4 (1985), 290–292 |
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1984 |
24. |
N. V. Krylov, “Estimates for derivatives of the solutions of nonlinear parabolic
equations”, Dokl. Akad. Nauk SSSR, 274:1 (1984), 23–26 |
25. |
N. V. Krylov, “Extremal properties of the solutions of stochastic equations”, Teor. Veroyatnost. i Primenen., 29:2 (1984), 209–221 ; Theory Probab. Appl., 29:2 (1985), 205–217 |
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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 ; 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 ; 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 ; Math. USSR-Sb., 48:2 (1984), 307–326 |
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1982 |
29. |
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 46:3 (1982), 487–523 ; 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 ; Russian Math. Surveys, 37:6 (1982), 81–105 |
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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 ; 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 ; Math. USSR-Izv., 19:1 (1982), 41–64 |
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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 ; Math. USSR-Izv., 16:1 (1981), 151–164 |
34. |
N. V. Krylov, T. P. Mirošničenko, “On extension of optimality set of Wald test”, Teor. Veroyatnost. i Primenen., 25:1 (1980), 167–171 ; Theory Probab. Appl., 25:1 (1980), 165–169 |
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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 |
36. |
N. V. Krylov, “On the theory of controlled diffusion processes”, Dokl. Akad. Nauk SSSR, 245:2 (1979), 298–300 |
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 |
38. |
N. V. Krylov, B. L. Rozovskii, “Stochastic evolution equations”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 14 (1979), 71–146 ; 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 ; Math. USSR-Sb., 37:1 (1980), 133–149 |
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 ; Theory Probab. Appl., 24:4 (1980), 772–781 |
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1978 |
41. |
N. V. Krylov, “On the limit passage in parabolic Bellman equations”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1417–1425 ; Math. USSR-Izv., 13:3 (1979), 677–684 |
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 ; Math. USSR-Izv., 13:2 (1979), 335–347 |
43. |
N. V. Krylov, B. L. Rozovskii, “On conditional distributions of diffusion processes”, Izv. Akad. Nauk SSSR Ser. Mat., 42:2 (1978), 356–378 ; 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 ; Math. USSR-Sb., 35:3 (1979), 351–362 |
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 ; 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 ; Math. USSR-Sb., 34:2 (1978), 161–171 |
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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 ; Math. USSR-Izv., 11:6 (1977), 1267–1284 |
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1976 |
48. |
N. V. Krylov, “The maximum principle for parabolic equations”, Uspekhi Mat. Nauk, 31:4(190) (1976), 267–268 |
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 ; Math. USSR-Sb., 29:2 (1976), 239–256 |
50. |
I. L. Genis, N. V. Krylov, “An example of a one-dimensional controlled process”, Teor. Veroyatnost. i Primenen., 21:1 (1976), 147–151 ; Theory Probab. Appl., 21:1 (1976), 148–152 |
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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 ; Math. USSR-Izv., 8:1 (1974), 233–254 |
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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 ; 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 ; 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 ; Theory Probab. Appl., 18:1 (1973), 54–63 |
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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 ; 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 ; Theory Probab. Appl., 17:1 (1972), 114–13 |
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1971 |
57. |
N. V. Krylov, “On the theory of nonlinear degenerating elliptic equations”, Dokl. Akad. Nauk SSSR, 201:6 (1971), 1279–1281 |
58. |
N. V. Krylov, “On uniqueness of the solution of Bellman's equation”, Izv. Akad. Nauk SSSR Ser. Mat., 35:6 (1971), 1377–1388 ; 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 ; 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 ; Theory Probab. Appl., 16:3 (1971), 438–448 |
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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 |
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 ; 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 ; Math. USSR-Sb., 10:1 (1970), 1–19 |
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1969 |
64. |
N. V. Krylov, “Parabolic equations on the plane and semigroups”, Differ. Uravn., 5:12 (1969), 2216–2224 |
65. |
N. V. Krylov, “Boundedly nonhomogeneous nonlinear elliptic and parabolic equations in the plane”, Uspekhi Mat. Nauk, 24:4(148) (1969), 201–202 |
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 ; 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 ; Theory Probab. Appl., 14:2 (1969), 330–336 |
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1967 |
68. |
N. V. Krylov, “The first boundary value problem for elliptic equations of second order”, Differ. Uravn., 3:2 (1967), 315–326 |
69. |
N. V. Krylov, “On the Green's function for the Dirichlet problem”, Uspekhi Mat. Nauk, 22:2(134) (1967), 116–118 |
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1966 |
70. |
N. V. Krylov, “On solutions of elliptic equations of the second order”, Uspekhi Mat. Nauk, 21:2(128) (1966), 233–235 |
71. |
N. V. Krylov, “Some properties of quasidiffusion process”, Uspekhi Mat. Nauk, 21:1(127) (1966), 177–179 |
72. |
N. V. Krylov, “On regular boundary points for Markov processes”, Teor. Veroyatnost. i Primenen., 11:4 (1966), 690–695 ; 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 ; Theory Probab. Appl., 11:3 (1966), 373–389 |
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1965 |
74. |
N. V. Krylov, A. A. Yushkevich, “Markov random sets”, Tr. Mosk. Mat. Obs., 13 (1965), 114–135 |
75. |
N. V. Krylov, “The Construction of an Optimal Strategy for a Finite Controlled Chain”, Teor. Veroyatnost. i Primenen., 10:1 (1965), 51–60 ; Theory Probab. Appl., 10:1 (1965), 45–54 |
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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 |
77. |
N. V. Krylov, A. A. Yuškevič, “On Markov Random Sets”, Teor. Veroyatnost. i Primenen., 9:4 (1964), 738–743 ; Theory Probab. Appl., 9:4 (1964), 666–670 |
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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 ; Theory Probab. Appl., 39:4 (1994), 654–656 |
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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 |
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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 |
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1972 |
81. |
N. V. Krylov, “Addendum: On Ito's Stochastic Integral Equations”, Teor. Veroyatnost. i Primenen., 17:2 (1972), 392–393 ; Theory Probab. Appl., 17:2 (1973), 373–374 |
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