Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 305--311

A BOSON FOCK SPACE REALIZATION OF ARCSINE BROWNIAN MOTION

By

K.R. PARTHASARATHY, Indian Statistical Institute, New Delhi

SUMMARY. Within the framework of conventional quantum stochastic calculus in a boson Fock space we obtain an explicit realization of the noncommutative arcsine Brownian motion which was constructed by Muraki (1997a) in a monotone Fock space and by Lu in an interacting free Fock space. This, at once, simplifies the theory of stochastic integration with respect to the arcsine Brownian motion.

AMS (1991) subject classification. 81S25.

Key words and phrases. Noncommutative Brownian motion, quantum Ito's formula.

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