Stochastic Processes and their Applications 145 204-225 2022年3月
We consider the heat equation with a dynamic potential [Formula presented]where N>2. Here the potential V is given by a Hardy-type function V(x,t)=λ|x−ξ(t)|−μ with constants λ,μ>0, and the singular point ξ(t) is a path of the N-dimensional fractio...
Journal of Mathematical Analysis and Applications 504(1) 2021年12月
We consider solutions of the linear heat equation in RN with isolated singularities. It is assumed that the position of a singular point depends on time and is Hölder continuous with the exponent α∈(0,1). We show that any isolated singularity is r...
Stochastic Processes and their Applications 130(1) 108-138 2020年1月
We investigate a problem suggested by Dembo, Peres, Rosen, and Zeitouni, which states that the growth exponent of favorite points associated with a simple random walk in Z2 coincides, on average and almost surely, with those of late points and hig...
As Dembo (In Lectures on Probability Theory and Statistics (2005) 1-101 Springer, and International Congress of Mathematicians, Vol. III (2006) 535-558, Eur. Math. Soc.) suggested, we consider the problem of late points for a simple random walk in...
大学院国際学術研究院