论文标题
没有随机控制问题引起的没有强大解决方案的SDE
SDEs with no strong solution arising from a problem of stochastic control
论文作者
论文摘要
我们研究了具有独特弱解决方案但没有强大解决方案的二维随机微分方程。我们表明，该SDE与Tsirelson的一维SDE示例具有显着属性，没有强大的解决方案。与具有非马克维亚漂移的Tsirelson方程相反，我们认为Markov Martingale具有Markovian扩散系数。我们表明，SDE没有强大的溶液，并且弱溶液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化的sar虫的随机控制问题的应用。
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.
