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Backward stochastic Schrödinger and infinite-dimensional Hamiltonian equations

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  • The paper is concerned with a semi-linear backward stochastic Schrödinger equation in $\mathbb{R}^d$ or in its bounded domain of a $C^2$ boundary. Galerkin's finite-dimensional approximation method is used and the harmonic role of the Laplacian is shown. The existence, uniqueness and regularity are given for the weak solution of the equation. A more general backward stochastic Hamiltonian partial differential equation is also discussed.
    Mathematics Subject Classification: 60H15, 35R60, 93E20, 37K99.


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