Strong limit of processes constructed from a renewal proces

2022/12/10 by Bardina, Xavier, Rovira, Carles · 2 citations
#60F15 60G15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.05312

Abstract

We construct a family of processes, from a renewal process, that have realizations that converge almost surely to the Brownian motion, uniformly on the unit time interval. Finally we compute the rate of convergence in a particular case.

Cited by

• Kac-Stroock type approximations for the Brownian motion
• Weak approximation for Gaussian processes from renewal processes

Related

• The complex Brownian motion as a strong limit of processes constructed from a Poisson process
• Weak approximation for Gaussian processes from renewal processes
• A note on the convergence of renewal and regenerative processes to a Brownian bridge
• Weak convergence of the integral of semi-Markov processes
• Limits of renewal processes and Pitman-Yor distribution