Estimates for multiple stochastic integrals and stochastic Hamilton-Jacobi equations
This paper is devoted to the study of stochastic Hamilton-Jacobi equation \[ dS+H \biggl(x,\frac{\partial S}{\partial x}\biggr)\,dt+c(x)\,d\xi_t=0,\quad x\in\mathbb{R}^d,\;t>0,\tag{1} \] and of the corresponding Hamilton system \[ \begin{aligned} dx&=\frac{\partial H}{\partial p}dt,\\ dp&=-\frac{\partial H}{\partial x}dt-\frac{\partial c}{\partial x}d\xi_t, \end{aligned}\tag{2} \] where \(\xi_t\) is a Lévy noise without Brownian part. The authors first prove the well-posedness of a suitable boundary value problem for (2), and then use this result to implement a stochastic version of the classical method of characteristics for Hamilton-Jacobi equation (1).
scientific article; zbMATH DE number 2110190