Quantum Stratonovich calculus and the quantum Wong-Zakai theorem
نویسندگان
چکیده
منابع مشابه
Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
We introduce the Stratonovich version of quantum stochastic calculus including integrals with respect to emission (creation), absorption (annihilation) and scattering (conservation) processes. The calculus allows us to consider the limit of regular open dynamical systems as a quantum Wong-Zakai approximation theorem. We introduce distinct definitions of Itô Dyson and Stratonovich Dyson time-ord...
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We extend the Itō-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Itō one and give conditions for th...
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Consider the heat equation driven by a smooth, Gaussian random potential: ∂tuε = 1 2 ∆uε + uε(ξε − cε), t > 0, x ∈ R, where ξε converges to a spacetime white noise, and cε is a diverging constant chosen properly. For any n > 1, we prove that uε converges in Ln to the solution of the stochastic heat equation. Our proof is probabilistic, hence provides another perspective of the general result of...
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The purpose of this paper is to establish the convergence in law of the sequence of “midpoint” Riemann sums for a stochastic process of the form f ′(W ), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-ofvariable formula in law with a second order correction term which is an Itô integral of f ′′(W ) with respect to...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2006
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2354331