Some estimates of the probability density of a stochastic integral

N. V. Krylov

doi:10.1070/IM1974v008n01ABEH002103

Some estimates of the probability density of a stochastic integral

N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Estimates in L_p 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.

Original language	English (US)
Pages (from-to)	233-254
Number of pages	22
Journal	Mathematics of the USSR - Izvestija
Volume	8
Issue number	1
DOIs	https://doi.org/10.1070/IM1974v008n01ABEH002103
State	Published - Feb 28 1974

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title = "Some estimates of the probability density of a stochastic integral",

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{\textquoteright}s nonlinear equations and the properties of λ convex functions.",

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AB - 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.

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Some estimates of the probability density of a stochastic integral

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