STOCHASTIC DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS DIFFUSION COEFFICIENTS

被引：0

作者：

Torres, Soledad ^{[1
]}

Viitasaari, Lauri ^{[2
]}

机构：

[1] Univ Valparaiso, Fac Ingn, CIMFAV, Valparaiso, Chile

[2] Uppsala Univ, Dept Math, Uppsala, Sweden

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2023年

关键词：

Stochastic differential equation; fractional calculus; Holder continuity; dis-continuity; bounded variation;

D O I：

10.1090/tpms/1201

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study one-dimensional stochastic differential equations of the form dX(t) = sigma(X-t)dY(t), where Y is a suitable Holder continuous driver such as the fractional Brownian motion B-H with H > 1/2. The innovative aspect of the present paper lies in the assumptions on diffusion coefficients sigma for which we assume very mild conditions. In particular, we allow sigma to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions.

引用

页码：159 / 175

页数：17

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