Stochastic differential equations driven by additive Volterra-Lévy and Volterra-Gaussian noises

2020/08/25 by Giulia Di Nunno, Di Nunno, Giulia, Yuliya Mishura +3
Economics, Econometrics and Finance · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2008.10854

openalex publication_date 2020/08/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by Lévy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is given to two kinds of Volterra-Gaussian processes that generalize the compact interval representation of fractional Brownian motion and to stochastic equations with such processes.

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