Asymptotic behaviour and functional limit theorems for a time changed Wiener process

2020/05/08 by Kondratiev, Yuri, Mishura, Yuliya, Schilling, René L.
#60F05 #60J55 #60J60 #60J65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2005.04122

Abstract

We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate state-space dependent intensity λ(x). Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time changed Wiener process. The normalization depends on the asymptotic behaviour of the intensity function λ. One of the possible limits is a skew Brownian motion.

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