Stochastic differential equations with discontinuous diffusion coefficients

IF 0.4 Q4 STATISTICS & PROBABILITY Theory of Probability and Mathematical Statistics Pub Date : 2023-10-03 DOI:10.1090/tpms/1201

Soledad Torres, Lauri Viitasaari

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引用次数: 0

Abstract

We study one-dimensional stochastic differential equations of the form d X t = σ ( X t ) d Y t dX_t = \sigma (X_t)dY_t , where Y Y is a suitable Hölder continuous driver such as the fractional Brownian motion B H B^H with H > 1 2 H>\frac 12 . The innovative aspect of the present paper lies in the assumptions on diffusion coefficients σ \sigma for which we assume very mild conditions. In particular, we allow σ \sigma to have discontinuities, and as such our results can be applied to study equations with discontinuous diffusions.

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具有不连续扩散系数的随机微分方程

我们研究了dX t = σ (X t)dY t dX＿t = \sigma (X＿t)dY＿t的一维随机微分方程，其中Y Y是一个合适的Hölder连续驱动器，如分数阶布朗运动B H B^H with H ＆gt;12 H＆gt;\frac本文的创新之处在于对扩散系数σ \sigma的假设，我们假设了非常温和的条件。特别地，我们允许σ \sigma具有不连续，因此我们的结果可以应用于研究具有不连续扩散的方程。

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Theory of Probability and Mathematical Statistics STATISTICS & PROBABILITY-

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1.30

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