Jump stochastic differential equations with non-Lipschitz and superlinearly growing coefficients

Yuchao Dong

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arXiv · 1605.05498

Jump stochastic differential equations with non-Lipschitz and superlinearly growing coefficients

Yuchao Dong

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Abstract

In the paper, we consider the no-explosion condition and pathwise uniqueness for SDEs driven by a Poisson random measure with coefficients that are super-linear and non-Lipschitz. We give a comparison theorem in the one-dimensional case under some additional condition. Moreover, we study the non-contact property and the continuity with respect to the space variable of the stochastic flow. As an application, we will show that there exists a unique strong solution for SDEs with coefficients like $x\log|x|$.

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Yuchao Dong. 2016-05-18. Jump stochastic differential equations with non-Lipschitz and superlinearly growing coefficients. https://arxiv.org/abs/1605.05498

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