2016/03/31 by Yizao Wang, Wang, Yizao
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1603.09685
openalex publication_date 2016/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the investigation of sample paths of q-Ornstein-Uhlenbeck process. We show that for all q∈(-1,1), the process has big jumps crossing from near one end point of the domain to the other with positive probability. Moreover, the number of such jumps in an appropriately enlarged window converges weakly to a Poisson random variable.