MCKEAN-VLASOV ITO-SKOROHOD EQUATIONS, AND NONLINEAR DIFFUSIONS WITH DISCRETE JUMP SETS

被引：72

作者：

GRAHAM, C ^{[1
]}

机构：

[1] ECOLE POLYTECH,CNRS,CAMP,URA 756,F-91128 PALAISEAU,FRANCE

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 1992年 / 40卷 / 01期

关键词：

POISSON POINT PROCESS; MCKEAN MEASURE; FIXED-POINT METHOD; PROPAGATION OF CHAOS;

D O I：

10.1016/0304-4149(92)90138-G

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a 'nonlinear' McKean-Vlasov Ito-Skorohod SDE, and develop a L(t) contraction scheme so as to get good results on the non-compensated jumps. We prove existence and uniqueness results under natural Lipachitz assumptions. We show that a wide class of nonlinear martingale problems, giving most diffusions with discrete jump sets, can be represented by SDEs satisfying our L1 assumptions, but not more classical L2 ones. We use this on a probabilistic model for a chromatographic tube. We finish by a propagation of chaos result on sample-paths.

引用

页码：69 / 82

页数：14