具有多元点过程和右上半连续障碍的反射BSDE的存在唯一性

IF 0.3 Q4 STATISTICS & PROBABILITY Random Operators and Stochastic Equations Pub Date : 2023-10-27 DOI:10.1515/rose-2023-2019
Baadi, Brahim, Marzougue, Mohamed
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引用次数: 0

摘要

摘要在具有可预测补偿器ν的多元点过程μ驱动的噪声中,证明了具有下障碍(ξ t) t∈[0,t] {(\xi_{t})_{t\ In [0, t]}}的反射后向随机微分方程解的存在唯一性,该方程被假设为右上半连续过程,但不一定是右连续过程,并具有Lipschitz驱动器f。利用可选强(但不一定是正确连续)超鞅的Mertens分解、Gal ' chouk和Lenglart对Itô公式的适当推广以及最优停止理论中的一些工具,建立了该结果。给出了这类方程的一个比较定理。
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Existence and uniqueness for reflected BSDE with multivariate point process and right upper semicontinuous obstacle
Abstract In a noise driven by a multivariate point process μ with predictable compensator ν, we prove existence and uniqueness of the reflected backward stochastic differential equation’s solution with a lower obstacle ( ξ t ) t [ 0 , T ] {(\xi_{t})_{t\in[0,T]}} which is assumed to be a right upper-semicontinuous, but not necessarily right-continuous process, and a Lipschitz driver f . The result is established by using the Mertens decomposition of optional strong (but not necessarily right continuous) super-martingales, an appropriate generalization of Itô’s formula due to Gal’chouk and Lenglart and some tools from optimal stopping theory. A comparison theorem for this type of equations is given.
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来源期刊
Random Operators and Stochastic Equations
Random Operators and Stochastic Equations STATISTICS & PROBABILITY-
CiteScore
0.60
自引率
25.00%
发文量
24
期刊最新文献
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