随机控制问题产生的无强解SDE

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-05-05 DOI:10.1214/23-ejp995

A. Cox, Benjamin A. Robinson

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引用次数: 3

摘要

我们研究了一个二维随机微分方程，它有一个唯一的弱解，但没有强解。我们证明了这个SDE与Tsirelson的没有强解的一维SDE的例子具有显著的性质。与具有非马尔可夫漂移的Tsirelson方程相反，我们考虑了具有马尔可夫扩散系数的强马尔可夫鞅。我们证明了SDE不存在强解，弱解的自然过滤是由布朗运动产生的。我们还讨论了我们的结果在径向对称环境中具有固定二次变分的鞅的随机控制问题上的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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SDEs with no strong solution arising from a problem of stochastic control

We study a two-dimensional stochastic differential equation that has a unique weak solution but no strong solution. We show that this SDE shares notable properties with Tsirelson's example of a one-dimensional SDE with no strong solution. In contrast to Tsirelson's equation, which has a non-Markovian drift, we consider a strong Markov martingale with Markovian diffusion coefficient. We show that there is no strong solution of the SDE and that the natural filtration of the weak solution is generated by a Brownian motion. We also discuss an application of our results to a stochastic control problem for martingales with fixed quadratic variation in a radially symmetric environment.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.