Feeling boundary by Brownian motion in a ball

2019/09/10 by Serafin, Grzegorz
#35K08 #60J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1909.04699

Abstract

We provide short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. The boundary behaviour is precisely described. Presented results may be considered as a complement or a generalization of the famous "principle of not feeling the boundary" in case of a ball.

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