Pointwise weak existence of distorted skew Brownian motion with respect to discontinuous Muckenhoupt weights

Abstract

For any starting point in ${\mathbb{R}}^d$, we identify the stochastic differential equation that is satisfied by distorted Brownian motion with respect to a certain discontinuous Muckenhoupt $A_2$-weight $\psi$. The discontinuities of $\psi$ typically take place on a sequence of level sets of the Euclidean norm $D_k:=\{x\in {\mathbb{R}}^d|\Vert x\Vert =d_k\}$, $k\in \mathbb{Z}$, where $(d_k{)}_{k\in \mathbb{Z}}\subset (0,\infty )$ may have accumulation points and each level set $D_k$ plays the role of a permeable membrane.

We corrected some inconsistemcies and added condition (H4)

References in corpus (1)

• On countably skewed Brownian motion with accumulation point

Cited by in corpus (1)

• On singular stochastic differential equations and Dirichlet forms