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Stochastic equations of non-negative processes with jumps

Zongfei Fu and Zenghu Li

Stochastic Processes and their Applications, 2010, vol. 120, issue 3, 306-330

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. Under suitable conditions, the comparison properties of solutions are proved. Those results are applied to construct continuous state branching processes with immigration as strong solutions of stochastic equations.

Keywords: Stochastic; equation; Strong; solution; Pathwise; uniqueness; Comparison; theorem; Non-Lipschitz; condition; Continuous; state; branching; process; Immigration (search for similar items in EconPapers)
Date: 2010
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Handle: RePEc:eee:spapps:v:120:y:2010:i:3:p:306-330