Problem of eigenvalues of stochastic Hamiltonian systems with boundary conditions

Shige Peng

Stochastic Processes and their Applications, 2000, vol. 88, issue 2, 259-290

Abstract: In this paper we solve problems of eigenvalues of stochastic Hamiltonian systems with boundary conditions and construct the corresponding eigenfunctions. This is a sort of forward-backward stochastic differential equations (FBSDE) parameterized by . The problem is to find non-trivial solutions while the trivial solution 0 exists. We show that, as the classical cases, the phenomenon of statistic periodicity and related stochastic oscillations appear. A method of dual transformation of stochastic Hamiltonian systems is introduced and applied, as a main tool, in the construction of eigenfunctions. This eigenvalue problem is also formulated in a standard way in functional analysis.

Keywords: Stochastic; Hamiltonian; systems; Dual; transformation; of; Hamiltonian; systems; Forward; and; backward; stochastic; differential; equations; Matrix-valued; Riccati; equations; Stochastic; vibration; Statistic; periodicity; Optimal; control (search for similar items in EconPapers)
Date: 2000
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