Stochastic Differential Equations and Inclusions with Mean Derivatives relative to the Past

Svetlana V. Azarina; Yuri E. Gliklikh

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Stochastic Differential Equations and Inclusions with Mean Derivatives relative to the Past

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摘要

We introduce and investigate a new sort of stochastic equations and inclusions given in terms of mean derivatives defined with respect to conditional expectation relative to the "past" sigma-algebra of a process. Some existence of solution results are proved. A new type of approximations to an upper semi-continuous set-valued mapping with convex compact values, point-wise converging to a measurable selector, is constructed and applied to investigation of inclusions with the above-mentioned derivatives.

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来源
《International Journal of Difference Equations》 |2012年第1期|27-41|共14页
作者
Svetlana V. Azarina; Yuri E. Gliklikh;
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作者单位

Voronezh State Technical University Department of Highest Mathematics and Physical and Mathematical Modelling Moskovsky prosp. 14, 394026 Voronezh, Russia;

Voronezh State University Mathematics Faculty Universitetskaya pl. 1, 394006 Voronezh, Russia;

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原文格式 PDF
正文语种英语
中图分类微分方程、积分方程;
关键词
Mean derivatives; "past" σ-algebra; stochastic differential equations; stochastic differential inclusions; approximations of set-valued mappings;

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Stochastic Differential Equations and Inclusions with Mean Derivatives relative to the Past

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