A Filtration of Wick Algebra and Its Application to Quantum SDEs
CaiShiWANG, ZhiYuanHUANG · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2004
A family of closed snbalgebras, indexed by R(the set of real numbers), of the Wick algebra is constructed. Fundamental properties of tile family are shown including the increasing property and the right-continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators.