Discontinuous Measure-Valued Branching Processes and Generalized Stochastic Equations |
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Authors: | Sylvie Mlard Sylvie Roelly |
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Institution: | Sylvie Méléard,Sylvie Roelly |
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Abstract: | We study a class of integrable and discontinuous measure-valued branching processes. They are constructed as limits of renormalized spatial branching processes, the underlying branching distribution belonging to the domain of attraction of a stable law. These processes, computed on a test function f, are semimartingales whose martingale terms are identified with integrals of f with respect to a martingale measure. According to a representation theorem of continuous (respectively purely discontinuous) martingale measures as stochastic integrals with respect to a white noise (resp. to a POISSON process), we prove that the measure-valued processes that we consider are solutions of stochastic differential equations in the space of L2 (Ω)-valued vector measures. |
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