A UNIFIED SYSTEM OF FB-SDES WITH LEVY JUMPS AND DOUBLE COMPLETELY-S SKEW REFLECTIONS
A UNIFIED SYSTEM OF FB-SDES WITH LEVY JUMPS AND DOUBLE COMPLETELY-S SKEW REFLECTIONS
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DOI：
10.4310/cms.2018.v16.n3.a4
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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：
--
作者：
Wanyang Dai
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 and 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 stricter boundary condition is imposed, i.e., the spectral radii of each square submatrix at a corner of the reflections are strictly less than unity, a unique adapted 6-tuple strong solution (in the sense of sample paths) is considered. In addition, as applications and economic 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.
