BROWNIAN BRIDGE IN QUANTUM PROBABILITY

Sinha, Kalyan B (2017) BROWNIAN BRIDGE IN QUANTUM PROBABILITY. In: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 48 (4). pp. 551-560.

PDF Ind_Jou_Pur_48-4_551_2017.pdf - Published Version Restricted to Registered users only Download (281kB) | Request a copy

Abstract

The Classical Brownian Bridge is constructed in Symmetric Fock space over an appropriate base Hilbert space. While the representation of the classical Ito-Wiener integral with respect to the increments of the Brownian bridge implements the unitary isomorphism between the Fock space and the (classical) L-2 space of the Brownian bridge (as is the case with the standard Brownian motion (SBM)), the quantum Ito-integrals with respect to the associated creation and annihilation bridge processes give different left-and right-integrals. This essentially displays the feature that the Brownian Bridge is not a process of independent increments.

Item Type:	Journal Article
Publication:	INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
Publisher:	10.1007/s13226-017-0245-4
Additional Information:	Copy right for this article belongs to the INDIAN NAT SCI ACAD, BAHADUR SHAH ZAFAR MARG, NEW DELHI 110002, INDIA
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	24 Jan 2018 10:10
Last Modified:	22 Oct 2018 12:14
URI:	http://eprints.iisc.ac.in/id/eprint/58868

Actions (login required)

View Item