@article{TVP_2011_56_1_a3,
author = {S. V. Shaposhnikov},
title = {On the uniqueness of a probabilistic solution of the {Cauchy} problem for the {Fokker{\textendash}Planck{\textendash}Kolmogorov} equation},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {77--99},
year = {2011},
volume = {56},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2011_56_1_a3/}
}
TY - JOUR AU - S. V. Shaposhnikov TI - On the uniqueness of a probabilistic solution of the Cauchy problem for the Fokker–Planck–Kolmogorov equation JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2011 SP - 77 EP - 99 VL - 56 IS - 1 UR - http://geodesic.mathdoc.fr/item/TVP_2011_56_1_a3/ LA - ru ID - TVP_2011_56_1_a3 ER -
S. V. Shaposhnikov. On the uniqueness of a probabilistic solution of the Cauchy problem for the Fokker–Planck–Kolmogorov equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 56 (2011) no. 1, pp. 77-99. http://geodesic.mathdoc.fr/item/TVP_2011_56_1_a3/
[1] Bogachev V. I., Krylov N. V., Röckner M., “On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions”, Comm. Partial Diff. Equations, 26:11–12 (2001), 2037–2080 | DOI | MR | Zbl
[2] Bogachev V. I., Da Prato G., Röckner M., “Existence of solutions to weak parabolic equations for measures”, Proc. London Math. Soc., 88:3 (2004), 753–774 | DOI | MR | Zbl
[3] Bogachev V. I., Da Prato G., Röckner M., Stannat W., “Uniqueness of solutions to weak parabolic equations for measures”, Bull. London Math. Soc., 39:4 (2007), 631–640 | DOI | MR | Zbl
[4] Röckner M., Zhang X., “Weak uniqueness of Fokker–Planck equations with degenerate and bounded coefficients”, C. R. Math. Acad. Sci. Paris, 348:7–8 (2010), 435–438 | MR
[5] Le Bris C., Lions P. L., “Existence and uniqueness of solutions to Fokker–Planck type equations with irregular coefficients”, Comm. Partial Differential Equations, 33 (2008), 1272–1317 | DOI | MR | Zbl
[6] Wu L., Zhang Y., “A new topological approach to the $L^{\infty}$-uniqueness of operators and $L^1$-uniqueness of Fokker–Planck equations”, J. Funct. Anal., 241 (2006), 557–610 | DOI | MR | Zbl
[7] Figalli A., “Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients”, J. Funct. Anal., 254:1 (2008), 109–153 | DOI | MR | Zbl
[8] Albeverio S., Bogachev V., Röckner M., “On uniqueness of invariant measures for finite- and infinite-dimensional diffusions”, Comm. Pure Appl. Math., 52 (1999), 325–362 | 3.0.CO;2-V class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[9] Bogachev V. I., Rëkner M., Shtannat V., “Edinstvennost reshenii ellipticheskikh uravnenii i edinstvennost invariantnykh mer diffuzii”, Matem. sb., 193:7 (2002), 3–36 | MR | Zbl
[10] Bogachev V. I., Rëkner M., Shaposhnikov S. V., “Globalnaya regulyarnost i otsenki reshenii parabolicheskikh uravnenii”, Teoriya veroyatn. i ee primen., 50:4 (2005), 652–674
[11] Bogachev V. I., Rëkner M., Shaposhnikov S. V., “Otsenki plotnostei statsionarnykh raspredelenii i perekhodnykh veroyatnostei diffuzionnykh protsessov”, Teoriya veroyatn. i ee primen., 52:2 (2007), 240–270
[12] Bogachev V. I., Rëkner M., Shaposhnikov S. V., “Polozhitelnye plotnosti perekhodnykh veroyatnostei diffuzionnykh protsessov”, Teoriya veroyatn. i ee primen., 53:2 (2008), 213–239
[13] Metafune G., Pallara D., Rhandi A., “Global properties of transition probabilities of singular diffusions”, Theory Probab. Appl., 54:1 (2009), 116–148 | MR | Zbl
[14] Spina C., “Kernel estimates for a class of Kolmogorov semigroups”, Arch. Math., 91:3 (2008), 265–279 | DOI | MR | Zbl
[15] Bogachev V. I., Krylov N. V., Rëkner M., “Ellipticheskie i parabolicheskie uravneniya dlya mer”, Uspekhi matem. nauk, 64:6 (2009), 5–116 | MR