Lévy driven linear and semilinear stochastic partial differential equations

2019/07/03 by David Berger, Berger, David
Economics, Econometrics and Finance · Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1907.01926

openalex publication_date 2019/07/03 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28

Abstract

The goal of this paper is twofold. In the first part we will study Lévy white noise in different distributional spaces and solve equations of the type p(D)s=q(D)L, where p and q are polynomials. Furthermore, we will study measurability of s in Besov spaces. By using this result we will prove that stochastic partial differential equations of the form p(D)u=g(⋅,u)+L have measurable solutions in weighted Besov spaces, where p(D) is a partial differential operator in a certain class, g:ℝ^d× ℂ→ ℝ satisfies some Lipschitz condition and L is a Lévy white noise.

Cited by

• Wavelet Analysis of the Besov Regularity of Lévy White Noises

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