$L^p(\Omega)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift

Dai Taguchi

$L^p(\Omega)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift

Probability 2014-04-10 v1

Authors: Dai Taguchi

Abstract

We consider a one-dimensional stochastic differential equations (SDE) with irregular coefficients. The purpose of this paper is to estimate the $L^p(\Omega)$ -difference of SDEs using the norm of the difference of coefficients, where the discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and H\"older continuous. As an application, we consider the stability problem.

Keywords

stochastic differential equations discontinuous drift one-sided lipschitz condition l^p-difference diffusion coefficient h\"older continuity stability

Cite

@article{arxiv.1404.2358,
  title  = {$L^p(\Omega)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift},
  author = {Dai Taguchi},
  journal= {arXiv preprint arXiv:1404.2358},
  year   = {2014}
}

Comments

22 pages

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