Reflecting Brownian Motion and the Gauss–Bonnet–Chern Theorem

The Semimartingale Structure of Reflecting Brownian Motion

We prove that reflecting Brownian motion on a bounded Lipschitz domain is a semimartingale. We also extend the well-known Skorokhod equation to this case. In this note we study the semimartingale property and the Skorokhod equation of reflecting Brownian motion on a bounded Euclidean domain. A R d_ valued continuous stochastic process X = {Xt ; t > 0} is said to be a semimartingale if it can be...

On Reflecting Brownian Motion with Drift

Let B = (Bt)t≥0 be a standard Brownian motion started at zero, and let μ ∈ R be a given and fixed constant. Set B t = Bt+μt and S t = max 0≤s≤t B s for t ≥ 0 . Then the process: (x ∨ Sμ)−Bμ = ((x ∨ S t )−B t )t≥0 realises an explicit construction of the reflecting Brownian motion with drift −μ started at x in R+ . Moreover, if the latter process is denoted by Z = (Z t )t≥0 , then the classic Lé...

Super-brownian Motion with Reflecting Historical Paths

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In p...

Super-Brownian motion with reflecting historical paths

Brownian Motion: The Link Between Probability and Mathematical Analysis

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