An improved uniqueness result for a system of stochastic differential equations related to the stochastic wave equation

C. Mueller; E. Neuman; M. Salins; G. Truong

An improved uniqueness result for a system of stochastic differential equations related to the stochastic wave equation

Probability 2019-09-16 v1

Authors: C. Mueller , E. Neuman , M. Salins , G. Truong

Abstract

We improve on the strong uniqueness results of [GLM+17], which deal with the following system of SDE. \begin{align*} dX_t&=Y_tdt \\ dY_t&=|X_{t}|^{\alpha}dB_t \end{align*} and $X_0=x_0,Y_0=y_0$ . For $(x_0,y_0)\ne(0,0)$ , we show that short-time uniqueness holds for $\alpha>-1/2$ .

Keywords

stochastic differential equations strong uniqueness short-time uniqueness stochastic wave equation alpha exponent

Cite

@article{arxiv.1909.05944,
  title  = {An improved uniqueness result for a system of stochastic differential equations related to the stochastic wave equation},
  author = {C. Mueller and E. Neuman and M. Salins and G. Truong},
  journal= {arXiv preprint arXiv:1909.05944},
  year   = {2019}
}

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8 pages

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