Lp solutions of general time interval BSDEs with generators satisfying a p-order weak stochastic-monotonicity condition

Xinying Li and Shengjun Fan

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 16, 5650-5676

Abstract: This article is interested in Lp (p>1) solutions of general time interval backward stochastic differential equations (BSDEs) with generator g satisfying a p-order weak stochastic-monotonicity condition and a general growth condition in y. An existence and uniqueness result of the Lp solution is proved for the multidimensional BSDEs where the generator g is stochastic-Lipschitz in z. And, a general comparison theorem and an existence and uniqueness theorem of the Lp solution is established for the one-dimensional BSDEs under a stochastic uniform-continuity condition of the generator g in z. These results strengthen some known works. The stochastic Gronwall-type inequality and the stochastic Bihari-type inequality play an important role in the whole article.

Date: 2023
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DOI: 10.1080/03610926.2021.2016833

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