Stochastic equations of non-negative processes with jumps

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 cont...

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Bibliographic Details
Published in:Stochastic processes and their applications 2010-03, Vol.120 (3), p.306-330
Main Authors: Fu, Zongfei, Li, Zenghu
Format: Article
Language:English
Subjects:
Comparison theorem
Continuous state branching process
Exact sciences and technology
Immigration
Markov processes
Mathematics
Non-Lipschitz condition
Pathwise uniqueness
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic analysis
Stochastic equation
Stochastic equation Strong solution Pathwise uniqueness Comparison theorem Non-Lipschitz condition Continuous state branching process Immigration
Stochastic processes
Strong solution
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2009.11.005