Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions (Communications in Mathematical Research, 2021)
In this paper, we investigate the eigenvalue problem of forward-backwarddoubly stochastic differential equations with boundary value conditions. We showthat this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, wecan characterize the eigenvalues exactly.
Keywords: doubly stochastic Hamiltonian system; eigenvalue problem; spectrum theory.