Time-Ordered Wick Exponential and Quantum Stochastic Differential Equations

Guo Jin-sheng

A class of generalized operator Wick filtration with R as its index set was constructed within the analysis framework of biparametric white noise.Fundamental properties of this Wick filtration were discussed.And a notion of adaptability of quantum stochastic processes in terms of generalized operators to the Wick filtration was introduced.The adaptive solution of a class of quantum stochastic differential equations to this Wick filtration was explored.

Franco Fagnola

Kazuo Takatsuka

CaiShiWANG, ZhiYuanHUANG

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.

Alexander Semenovich Holevo

Alexander Semenovich Holevo

The rigorous definition of time-ordered exponentials, solving quantum linear stochastic differential equations, is extended to Boson and Fermion stochastic calculi with infinitely many degrees of freedom. The relation to the classicalmultiplicative stochastic integral, solving the Doleans exponential equation, is discussed.