Multidimensional Quantum Stochastic Integrals

Abstract

Quantum stochastic analogues (ℋ,script A,{script A} ,m,ℝ), of a classical stochastic base may be formed whereby a classical sample space Ω is replaced by a Hilbert Space ℋ, σ-field ℱ is replaced by a von Neumann algebra script C, the filtration {ℱ} by a filtration {script C} of von Neumann subalgebras of the von Neumann algebra script C and the probability measure ℘ with gage m [1]. In this presentation we consider quantum analogues for multidimensional stochastic processes, extending quantum results in [2, 3, 4, 5, 6, 7, 8].