Abstract:
In this paper, two estimates, (4) and (11), are proved. In (4), xt=∫t0σsdξs+∫t0bsds here ξs is an n-dimensional Wiener process, bs=ks+σshs, and ks, hs satisfy the conditions a), б) (dt=detσ2t). A particular case of (11) is (5).
Citation:
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
\Bibitem{Kry73}
\by N.~V.~Krylov
\paper Some estimates in the theory of stochastic integral
\jour Teor. Veroyatnost. i Primenen.
\yr 1973
\vol 18
\issue 1
\pages 56--65
\mathnet{http://mi.mathnet.ru/tvp2680}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=310969}
\zmath{https://zbmath.org/?q=an:0284.60053}
\transl
\jour Theory Probab. Appl.
\yr 1973
\vol 18
\issue 1
\pages 54--63
\crossref{https://doi.org/10.1137/1118004}
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https://www.mathnet.ru/eng/tvp2680
https://www.mathnet.ru/eng/tvp/v18/i1/p56
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Paul-André Meyer, Glenn Shafer, Trends in the History of Science, The Splendors and Miseries of Martingales, 2022, 169
Pierre-Louis Lions, North-Holland Mathematical Library, 32, Stochastic Analysis, Proceedings of the Taniguchi International Symposium on Stochastic Analysis, 1984, 333
P. L. Lions, “On the Hamilton-Jacobi-Bellman equations”, Acta Appl Math, 1:1 (1983), 17
N. V. Krylov, “Boundedly nonhomogeneous elliptic and parabolic equations”, Math. USSR-Izv., 20:3 (1983), 459–492
M. Yor, Lecture Notes in Mathematics, 876, Ecole d'Eté de Probabilités de Saint-Flour IX-1979, 1981, 239
N. V. Krylov, “Some estimates of the probability density of a stochastic integral”, Math. USSR-Izv., 8:1 (1974), 233–254
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