On countably skewed Brownian motion with accumulation point

Abstract

In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a sequence of points that has exactly one accumulation point in $\mathbb{R}$. The considered process is identified as special distorted Brownian motion $X$ in dimension one and is studied thoroughly. Besides strong uniqueness, we present necessary and sufficient conditions for non-explosion, recurrence and positive recurrence as well as for $X$ to be semimartingale and possible applications to advection-diffusion in layered media.

Revised version

References in corpus (2)

• On the constructions of the skew Brownian motion
• Explicit recurrence criteria for symmetric gradient type Dirichlet forms satisfying a Hamza type condition

Cited by in corpus (7)

• Recurrence criteria for generalized Dirichlet forms
• Explicit recurrence criteria for symmetric gradient type Dirichlet forms satisfying a Hamza type condition
• On general skew Brownian motions
• The weak rate of convergence for the Euler-Maruyama approximation of one-dimensional stochastic differential equations involving the local times of the unknown process
• Pointwise weak existence of distorted skew Brownian motion with respect to discontinuous Muckenhoupt weights
• An explicit representation of the transition densities of the skew Brownian motion with drift and two semipermeable barriers
• Bi-Directional Grid Constrained Stochastic Processes' Link to Multi-Skew Brownian Motion