Strong limit of processes constructed from a renewal process-Reference-Cited by-同舟云学术

Strong limit of processes constructed from a renewal process

Published:2023-01-01 Issue:1 Volume:21 Page:
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Bardina Xavier¹,Rovira Carles²

Affiliation:

1. Department of Matemàtiques, Edifici C, Universitat Autònoma de Barcelona , 08193 Bellaterra , Spain

2. Facultat de Matemàtiques, Universitat de Barcelona , Gran Via 585 , 08007 Barcelona , Spain

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2023-0112/pdf

Reference12 articles.

1. M. Kac, A stochastic model related to the telegrapher’s equation, Rocky Moutain J. Math. 4 (1974), no. 3, 497–509, DOI: https://doi.org/10.1216/RMJ-1974-4-3-497.

2. R. J. Griego, D. Heath, and A. Ruiz-Moncayo, Almost sure convergence of uniform transport processes to Brownian motion, Ann. Math. Stat. 42 (1971), no. 3, 1129–1131, DOI: https://doi.org/10.1214/aoms/1177693346.

3. L. G. Gorostiza and R. J. Griego, Rate of convergence of uniform transport processes to Brownian motion and application to stochastic integrals, Stochastics 3 (1980), no. 1-4, 291–303, DOI: https://doi.org/10.1080/17442508008833152.

4. M. Csörgő and L. Horváth, Rate of convergence of transport processes with an application to stochastic differential equations, Probab. Theory Related Fields 78 (1988), no. 3, 379–387, DOI: https://doi.org/10.1007/BF00334201.

5. G. T. Nguyen and O. Peralta, An explicit solution to the Skorokhod embedding problem for double exponential increments, Statist. Probab. Lett. 165 (2020), 108867, DOI: https://doi.org/10.1016/j.spl.2020.108867.