$L^p$ Solutions of Backward Stochastic Differential Equations with Jumps

Song Yao

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arXiv · 1007.2226

$L^p$ Solutions of Backward Stochastic Differential Equations with Jumps

Song Yao

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Abstract

Given $p \in (1, 2)$, we study $L^p$-solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in $(y,z)-$variables. We show that such a BSDEJ with a p-integrable terminal data admits a unique $L^p$ solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.

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Song Yao. 2010-07-13. $L^p$ Solutions of Backward Stochastic Differential Equations with Jumps. https://arxiv.org/abs/1007.2226

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