Abstract
Let $(\Omega, \mathscr{J}, P; \mathscr{J}_{s,t})$ be a probability space with a family of sub-$\sigma$-algebras indexed by $(s, t) \in \lbrack 0, \infty) \times \lbrack 0, \infty)$, satisfying the usual conditions. Let $X(s,t)$ be a solution of a stochastic differential equation in the plane with respect to the Wiener-Yeh process. Under one of the usual conditions used to guarantee existence and uniqueness of a solution to the equation, it is shown that the absolute moments of $X(s,t)$ grow at most exponentially in $st$. The estimate is based on a version of the two parameter Ito formula and on an extension of Gronwall's inequality to functions of two variables.
Citation
J. Reid. "Estimate on Moments of the Solutions to Stochastic Differential Equations in the Plane." Ann. Probab. 11 (3) 656 - 668, August, 1983. https://doi.org/10.1214/aop/1176993510
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