On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise

2013/06/02 by Andrey Pilipenko, Pilipenko, Andrey
Economics, Econometrics and Finance · Engineering · Mathematics · #60H10 #60J75 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1306.0212

openalex publication_date 2013/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

One-dimensional stochastic differential equations with additive Lévy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a Lévy symmetric stable process with α∈(1;2), then the measurability and boundedness of a drift term is sufficient for the existence of a strong solution. We also study continuous dependence of the strong solution on the initial value and the drift.

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