Stochastic Integration on the Full Fock Space with the Help of a Kernel Calculus | Zendy

Roland Speicher | Zendy

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Stochastic Integration on the Full Fock Space with the Help of a Kernel Calculus

Author(s) -

Roland Speicher

Publication year - 1991

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195170235

Subject(s) - fock space , mathematics , kernel (algebra) , bounded function , quantum stochastic calculus , stochastic calculus , stochastic differential equation , banach space , pure mathematics , class (philosophy) , fock state , algebra over a field , space (punctuation) , stochastic partial differential equation , mathematical analysis , differential equation , quantum mechanics , computer science , physics , quantum process , artificial intelligence , quantum dynamics , quantum , operating system

We develop a stochastic integration theory with respect to creation, annihilation and gauge operators on the full Fock space. This is done by using a kernel representation for a large class of bounded operators on the full Fock space. It is shown that the kernels form a Banach algebra. Having established the definition of processes and stochastic integrals we go on to prove an Ito formula and use this for examining stochastic evolutions and constructing dilations of special completely positive semigroups. Explicit solutions of the corresponding stochastic differential equations are given.

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