Quantum Lévy-type Laplacian and associated stochastic differential equations
Volume 73 / 2006
Banach Center Publications 73 (2006), 81-97
MSC: Primary 60H40; Secondary 46A32, 46F25, 46G20.
DOI: 10.4064/bc73-0-5
Abstract
We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.
