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2007•Communications on Stochastic AnalysisOpen access

Quantum stochastic calculus on interacting Fock spaces: semimartingale estimates and stochastic integral

Vitonofrio Crismale

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Abstract

A quantum stochastic integration theory on interacting Fock spaces (IFS) is developed.We present the semi-martingale inequalities either in standard general IFS or in 1-mode type IFS, which allow us to introduce the definitions of integrable processes and construct stochastic integrals satisfying some useful properties which will be presented in [13].

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A quantum stochastic integration theory on interacting Fock spaces (IFS) is developed.We present the semi-martingale inequalities either in standard general IFS or in 1-mode type IFS, which allow us to introduce the definitions of integrable processes and construct stochastic integrals satisfying some useful properties which will be presented in [13].

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Available abstract

A quantum stochastic integration theory on interacting Fock spaces (IFS) is developed.We present the semi-martingale inequalities either in standard general IFS or in 1-mode type IFS, which allow us to introduce the definitions of integrable processes and construct stochastic integrals satisfying some useful properties which will be presented in [13].

Key concepts: Semimartingale, Quantum stochastic calculus, Stochastic calculus, Fock space, Stratonovich integral, Mathematics, Malliavin calculus, Calculus (dental)

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