On the existence and uniqueness of solutions to stochastic differential equations of mixed Brownian and Poissonian sheet type

Jicheng Liu

Stochastic Processes and their Applications, 2001, vol. 94, issue 2, 339-354

Abstract: Let be a two-parameter semimartingale, where M is a continuous martingale, [Lambda] is the character of the Poisson point measure Y, N=Y-[Lambda], we prove that f(Xz) is expressible as such a sum once again via the partial differentiation formula, where f is a twice continuously differentiable function. Then, we prove a new theorem on the existence and uniqueness of solutions to the mixed Brownian and Poissonian sheet type stochastic differential equations with non-Lipschitz coefficients by applying the partial differentiation formula.

Keywords: Two-parameter; mixed; type; SDE; Two-parameter; martingale; Two-parameter; Poisson; process; Gronwall-Bellman's; lemma (search for similar items in EconPapers)
Date: 2001
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