The martingale problem for a class of nonlocal operators of diagonal type

Jamil Chaker

Mathematische Nachrichten, 2019, vol. 292, issue 11, 2316-2337

Abstract: We consider systems of stochastic differential equations of the form dXti=∑j=1dAij(Xt−)dZtjfor i=1,⋯,d with continuous, bounded and non‐degenerate coefficients. Here Zt1,⋯,Ztd are independent one‐dimensional stable processes with α1,⋯,αd∈(0,2). In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices.

Date: 2019
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https://doi.org/10.1002/mana.201800452

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