Approximations of a complex Brownian motion with processes constructed from a process with independent increments

2013/08/27 by Xavier Bardina, Bardina, Xavier, Carles Rovira +1
Economics, Econometrics and Finance · Mathematics · #60F17 #60G15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60F17 #msc:60G15

paper · pdf · doi:10.48550/arxiv.1308.5854

arxiv created 2013/08/27 · openalex publication_date 2013/08/27 · arxiv updated 2013/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments. We give sufficient conditions for the characteristic function of the process with independent increments that ensure the existence of the approximation. We apply these results to Lévy processes. Finally we extend this results to the m-dimensional complex Brownian motion.

Related

• The complex Brownian motion as a strong limit of processes constructed from a Poisson process
• Discrete approximation of a stable self-similar stationary increments process
• A note on recovering the Brownian motion component from a Levy process
• Weak approximation for Gaussian processes from renewal processes
• Brownian motion in riemannian admissible complex