Strong Feller Property of Sticky Reflected Distorted Brownian Motion

The Strong Markov Property of the Brownian Motion

Traps for Reflected Brownian Motion

Consider an open set D ⊂ R, d ≥ 2, and a closed ball B ⊂ D. Let E TB denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x ∈ D. We say that D is a trap domain if supx E TB = ∞. A domain D is not a trap domain if and only if the reflecting Brownian motion in D is uniformly ergodic. We fully characterize the simply connected planar trap domains using a...

Lecture 22: Reflected brownian motion

We use the following technical facts. If x is a Lipschitz continuous, then it also has derivative everywhere except measure zero set of points on [0, ∞) and t x(t) = ẋ(u)du. Note, however that if x is a realization of a Brownian motion, 0 then it is nowhere differentiable and we cannot write this integral representation. Also if x is a continuous and non-decreasing, then it has derivatives almo...

Regime-switching diffusion processes: strong solutions and strong Feller property

We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established under the general assumption that the diffusion in every fixed environment has a unique non-explosive strong solution. Moreover, non-explosio...

Limiting Behaviors for Brownian Motion Reflected on Brownian Motion

Suppose that g(t) and Wt are independent Brownian motions starting from g(0) = W0 = 0. Consider the Brownian motion Yt reflected on g(t), obtained from Wt by the means of the Skorohod lemma. The upper and lower limiting behaviors of Yt are presented. The upper tail estimate on exit time is computed via principal eigenvalue.