BSDE associated with Lévy processes and application to PDIE

[摘要] We deal with backward stochastic differential equations (BSDE for short) driven byTeugel's martingales and an independent Brownian motion. We study the existence,uniqueness and comparison of solutions for these equations under a Lipschitz as well asa locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we provethat if the Lipschitz constantLNbehaves aslog(N)in the ballB(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differentialintegral equations (PDIE for short).

[学科分类] 应用数学