Abstract Cauchy Problems in separable Banach Spaces driven by random Measures: Existence and Uniqueness

2017/10/04 by Alexander Nerlich, Nerlich, Alexander · 1 citation
Economics, Econometrics and Finance · #35A01 #35A02 #47J35 #60H15 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1710.01796

openalex publication_date 2017/10/04 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study stochastic evolution inclusions of the form η(t,z) N_Θ(dt ⊗ z)∈ dX(t)+A X(t)dt, where A is a multi-valued operator acting on a separable Banach space and N_Θ is the counting measure induced by a point process Θ. Firstly, we will set up the concepts of strong and mild solutions; then we will derive existence as well as uniqueness criteria for these kinds of solutions and give a representation formula for the solutions. The results will be formulated by means of nonlinear semigroup theory and except for separability, no assumptions on the underlying Banach space are required.

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