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Stochastic equations of non-negative processes with jumps. (English) Zbl 1184.60022
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.

MSC:
60H20 Stochastic integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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