A note on existence of global solutions and invariant measures for jump\n SDEs with locally one-sided Lipschitz drift

2016/12/12 by Mateusz B. Majka, Majka, Mateusz B.
Economics, Econometrics and Finance · #Climate Change Policy and Economics #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1612.03824

openalex publication_date 2016/12/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We extend some methods developed by Albeverio, Brze 'zniak and Wu and we\nshow how to apply them in order to prove existence of global strong solutions\nof stochastic differential equations with jumps, under a local one-sided\nLipschitz condition on the drift (also known as a monotonicity condition) and a\nlocal Lipschitz condition on the diffusion and jump coefficients, while an\nadditional global one-sided linear growth assumption is satisfied. Then we use\nthese methods to prove existence of invariant measures for a broad class of\nsuch equations.\n

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