Stochastic equations of non-negative processes with jumps

2008/02/07 by Zongfei Fu, Fu, Zongfei, Zenghu Li +1 · 3 citations
Economics, Econometrics and Finance · Mathematics · #60H10 #60H20 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0802.0933

openalex publication_date 2008/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under suitable conditions. The results are applied to stochastic equations driven by one-sided Levy processes and those of continuous state branching processes with immigration.

Cited by

• Boundary behavior of continuous-state interacting multi-type branching processes with immigration
• A Fluctuation Limit Theorem of Branching Processes with Immigration and Statistical Applications
• Convergence to a Continuous State Branching Process with jumps and Height Process

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