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.