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Stability problem for one-dimensional stochastic differential equations with discontinuous drift. (English) Zbl 1367.60085

Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLVIII. Cham: Springer (ISBN 978-3-319-44464-2/pbk; 978-3-319-44465-9/ebook). Lecture Notes in Mathematics 2168. Séminaire de Probabilités, 97-121 (2016).
Summary: We consider one-dimensional stochastic differential equations (SDEs) with irregular coefficients. The goal of this paper is to estimate the \(L^p(\Omega)\)-difference between two SDEs using a norm associated to the difference of coefficients. In our setting, the (possibly) discontinuous drift coefficient satisfies a one-sided Lipschitz condition and the diffusion coefficient is bounded, uniformly elliptic and Hölder continuous. As an application of this result, we consider the stability problem for this class of SDEs.
For the entire collection see [Zbl 1359.60007].

MSC:

60H20 Stochastic integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
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