Weak approximation for Gaussian processes from renewal processes
Abstract
In [Citation5] a family of processes that converge strongly toward Brownian motion, defined from renewal processes, are constructed. In this paper we prove that some of these processes can be utilized to build approximations of Gaussian processes such as fractional Brownian motion or multiple Stratonovich integrals and we provide sufficient conditions on renewal processes to ensure that the convergence holds. An illustrative example of such a Gaussian process is the fractional Brownian motion with any Hurst parameter.
Fields of Study & Subjects
Stochastic processes and financial applications
Financial Risk and Volatility Modeling
Analysis of environmental and stochastic processes
Publication details
- Journal / source
- Stochastic Analysis and Applications
- Publisher
- Informa UK Limited
- Volume
- 44
- Issue
- 4
- Pages
- 417–428
- Publication date
- 15 May 2026
- Language
- EN