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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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##### References:
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