Abstract:
Estimates in Lp are derived for probability densities of stochastic integrals. An example is presented which shows that for some values of p such estimates are not attainable. The method of proving these estimates is based on a study of Bellman's nonlinear equations and the properties of λ-convex functions.
\Bibitem{Kry74}
\by N.~V.~Krylov
\paper Some estimates of the probability density of a~stochastic integral
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 1
\pages 233--254
\mathnet{http://mi.mathnet.ru/eng/im1899}
\crossref{https://doi.org/10.1070/IM1974v008n01ABEH002103}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=345206}
\zmath{https://zbmath.org/?q=an:0293.60049}
Linking options:
https://www.mathnet.ru/eng/im1899
https://doi.org/10.1070/IM1974v008n01ABEH002103
https://www.mathnet.ru/eng/im/v38/i1/p228
This publication is cited in the following 23 articles:
Theory Probab. Appl., 68:3 (2023), 510–536
N. V. Krylov, “On Diffusion Processes with Drift in a Morrey Class Containing Ld+2”, J Dyn Diff Equat, 35:4 (2023), 2813
N. V. Krylov, “On diffusion processes with drift in Ld”, Probab. Theory Relat. Fields, 179:1-2 (2021), 165
N. V. Krylov, “Weighted Parabolic Aleksandrov Estimates: PDE and Stochastic Versions”, J Math Sci, 244:3 (2020), 419
Guanting Chen, Alex Shkolnik, Kay Giesecke, 2020 Winter Simulation Conference (WSC), 2020, 277
Nicolas Champagnat, Pierre-Emmanuel Jabin, “Strong solutions to stochastic differential equations with rough coefficients”, Ann. Probab., 46:3 (2018)
Alexey Rudenko, “Some properties of the Itô–Wiener expansion of the solution of a stochastic differential equation and local times”, Stochastic Processes and their Applications, 2012
B. Jourdain, Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, 197
N.V. Krylov, R. Liptser, “On diffusion approximation with discontinuous coefficients”, Stochastic Processes and their Applications, 102:2 (2002), 235
R. Mikulevicius, B. Rozovskii, “Linear Parabolic Stochastic PDE and Wiener Chaos”, SIAM J Math Anal, 29:2 (1998), 452
Ping Gao, Seminar on Stochastic Processes, 1992, 1993, 135
Nigel J. Cutland, “Infinitesimal methods in control theory: Deterministic and stochastic”, Acta Appl Math, 5:2 (1986), 105
N. V. Krylov, “On estimates of the maximum of a solution of a parabolic equation and estimates of the distribution of a semimartingale”, Math. USSR-Sb., 58:1 (1987), 207–221
Pure and Applied Mathematics, 122, 1986, 107
Nigel J. Cutland, “Simplified existence for solutions to stochastic differential equations”, Stochastics, 14:4 (1985), 319
P. L. Lions, “On the Hamilton–Jacobi–Bellman equations”, Acta Appl Math, 1:1 (1983), 17
P.-L. Lions, “A remark on Bony maximum principle”, Proc. Amer. Math. Soc., 88:3 (1983), 503
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