On integration with respect to the q-Brownian motion

Abstract

For a parameter 0<q<1, we use the Jackson q-integral to define integration with respect to the so called q-Brownian motion. Our main results are the q-analogs of the L_2-isometry and of the Ito formula for polynomial integrands. We also indicate how the L_2-isometry extends the integral to more general functions.

This is an expanded version of the paper

References in corpus (1)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue