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Stochastic equations of non-negative processes with jumps

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  • Fu, Zongfei
  • Li, Zenghu

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.

Suggested Citation

  • Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:3:p:306-330
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    References listed on IDEAS

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    1. Bass, Richard F. & Burdzy, Krzysztof & Chen, Zhen-Qing, 2004. "Stochastic differential equations driven by stable processes for which pathwise uniqueness fails," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 1-15, May.
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