Stochastic integral representations of quantum martingales on multiple Fock space
نویسنده
چکیده
In this paper a quantum stochastic integral representation theorem is obtained for unbounded regular martingales with respect to multidimensional quantum noise. This simultaneously extends results of Parthasarathy and Sinha to unbounded martingales and those of the author to multidimensions.
منابع مشابه
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space h and it is shown that they satisfy similar properties as the derivation and divergence operator on the Wiener space over h. The derivation operator is then used to give sufficient conditions for the existence of smooth Wig...
متن کاملChaotic States and Stochastic Integration in Quantum Systems
Quantum chaotic states over a noncommutative monoid, a unitalization of a noncommutative Ito algebra parametrizing a quantum stochastic Levy process, are described in terms of their infinitely divisible generating functionals over the simple monoid-valued fields on an atomless ‘space-time’ set. A canonical decomposition of the logarithmic conditionally posive-definite generating functional is c...
متن کاملAn analytic double product integral
The double product integral →← ∏ (1+λ(dA†⊗dA−dA⊗dA†)) is constructed as a family of unitary operators in double Fock space satisfying quantum stochastic differential equations with unbounded operator coefficients.
متن کاملBoson-Fermion unification implemented by Wick calculus
We construct a transformation between Bose Fock space Γ+ (h) and Fermi Fock space Γ − (h) that is super-symmetric in the sense that it converts Boson fields into Fermi fields over a fixed one-particle space h. The transformation involves the spectral splitting of h into a continuous direct integral of internal spaces (kω) ω . We intoduce a new theory of integration on the Fock spaces over L ( (...
متن کاملAppell Polynomials and Their Relatives
This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003