The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a u...The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.展开更多
With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, ...With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, many researches on this subject have been taken. However, they are usually applied to two-dimensional cases. For the three-dimensional ones, very few analyses have been done because of the great complexity on mathematics and mechanics. In this study, based on the point-force solutions for two perfectly展开更多
文摘The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.
基金National Natural Science Foundation of Chinathe National Ph.D. Foundation
文摘With the rapidly increasing use of composite materials, a great deal of interest in the interface crack has been generated among the technicians, metal physicists and materials scientists. To the authors’ knowledge, many researches on this subject have been taken. However, they are usually applied to two-dimensional cases. For the three-dimensional ones, very few analyses have been done because of the great complexity on mathematics and mechanics. In this study, based on the point-force solutions for two perfectly
