A unified system of FB-SDEs with Levy jumps and double completely-S skew reflections


题目:A unified system of FB-SDEs with Levy jumps

and double completely-S skew reflections

报告人:戴万阳 教授南京大学

时 间:2018531日(周四)上午10:30-11:30

地 点:数学学院A302



戴万阳南京大学数学系教授(博导/重要学科岗)江苏金融科技研究中心特邀专家、江苏省概率统计学会理事长、国家多个概率统计运筹管理及工业与应用数学学会副理事长等、国家自然科学奖励委员会数学学科会评委员(随机分析组组长)、国家自然科学基金重大/重点(包括杰出青年/优秀青年)项目评审专家; Journal of Advances in Applied Mathematics主编,多次担任国际大会主席;曾任美国电信贝尔实验室永久科学家与研究员。在量子云计算、随机网络反射扩散逼近、随机(渐近)最优控制与(随机微分)博弈论及 (正倒向与反射)随机(/)微分方程等领域作了多项重要系列工作


报告摘要:We study the well-posedness of a unified system of coupled forward-backward stochastic differential equations (FB-SDEs) with Levy jumps and double completely-S skew reflections. Owing to the reflections, the solution to an embedded Skorohod problem may be not unique. Thus, we develop a weak convergence method to prove the well-posedness of an adapted 6-tuple weak solution in the sense of distribution to the unified system. The proof heavily depends on newly established Malliavin calculus for vector-valued Levy processes together with a generalized linear growth and Lipschitz condition that guarantees the well-posedness of the unified system even under a random environment. Nevertheless, if a more strict boundary condition is imposed, a unique adapted 6-tuple strong solution in the sense of sample pathwise is concerned. In addition, as applications and economical studies of our unified system, we also develop new techniques including deriving a generalized mutual information formula for signal processing over possible non-Gaussian channels with multi-input multi-output (MIMO) antennas and dynamics driven by Levy processes.