Articlegreen2015

Stochastic flow for SDEs with jumps and irregular drift term

26 citations0/0 files storedBanach Center Publications

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stochastic processes and statistical mechanics

Abstract

We consider non-degenerate SDEs with a $\beta$-Hölder continuous and bounded drift term and driven by a Lévy noise $L$ which is of $\alpha$-stable type. If $\beta > 1 - \frac{\alpha}{2} $ and $\alpha \in [1,2)$, we show pathwise uniqueness and existence

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References

2004Lévy Processes and Stochastic Calculus 1981ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS 2005Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering 2007Uniqueness of Solutions of Stochastic Differential Equations 2012PATHWISE UNIQUENESS FOR SINGULAR SDEs DRIVEN BY STABLE PROCESSES 2011Pathwise uniqueness and continuous dependence for SDEs with non-regular drift 2013Strong uniqueness for stochastic evolution equations in Hilbert spaces perturbed by a bounded measurable drift 2005Systems of equations driven by stable processes

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2019Gradient estimates and ergodicity for SDEs driven by multiplicative Lévy noises via coupling

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