A unified system of FB-SDEs with Levy jumps and double completely-S skew refelections
A unified system of FB-SDEs with Levy jumps and double completely-S skew refelections
复制标题
具有 Levy 跳跃和双完全 S 偏斜反射的 FB-SDE 统一系统
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Wanyang Dai
中科院分区：
文献类型：
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作者：
Wanyang Dai
研究了具有Levy跳和双完全S斜反射的耦合正倒向随机微分方程统一系统的适定性。由于反射，嵌入式Skorohod问题的解决方案可能不是唯一的，即，分支可能发生在反射边界，著名的压缩映射方法不能直接扩展到解决我们的问题。因此，我们发展了一个弱收敛方法来证明一个适应的6元组弱解在分布意义下对统一系统的适定性。证明严重依赖于新建立的Malliavin演算向量值Levy过程连同广义线性增长和Lipschitz条件，保证了即使在随机环境下的统一系统的适定性。然而，如果施加更严格的边界条件，即，当反射的谱半径在一定意义下严格小于1时，得到了一个在样本路径意义下的唯一的自适应六元组强解。此外，作为我们的统一系统的应用和经济研究，我们还开发了新的技术，包括推导出一个广义互信息公式的信号处理可能的非高斯信道与多输入多输出（MIMO）天线和动力学驱动的Levy过程。
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, i.e., bifurcations may occur at reflection boundaries, the well-known contraction mapping approach can not be extended directly to solve our problem. 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, i.e., the spectral radii in certain sense for the reflections are strictly less than the unity, 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.