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Anticipating quantum stochastic integrals

Department of Mathematics, Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea

E-mail Address: uncigji@chungbuk.ac.kr

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https://doi.org/10.1142/S0219025724400071Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue: Special Commemorative Issue in Honour of Professor K R Parthasarathy – I
Guest Editors: Amarjit Budhiraja and Arup Kumar Pal

Abstract

Based on the quantum white noise theory, we formulate new types of anticipating quantum stochastic integrals by combining the Hitsuda–Skorokhod quantum stochastic integrals and the interactions between the integrands and the integrators. For our purpose, we prove various versions of analytic characterization theorems of symbols of white noise operators as more general cases. Also, several types of quantum (stochastic) gradients are formulated as continuous linear operators which are related to the quantum white noise derivatives and reflecting the interactions with the external noises. Finally, we formulate further systematical study of anticipating quantum stochastic integrals.

Communicated by Arup Kumar Pal

In the memory of Professor K. R. Parthasarathy.

Keywords:

AMSC: 81S25, 60H40, 46F25

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