q-Deformed Brownian Motion
V. I. Man'ko, R. Vilela Mendes
TL;DR
This paper introduces q-deformed Brownian motion by extending classical Brownian motion within a q-deformed algebraic framework, highlighting its non-Gaussian properties and cumulant structure.
Contribution
It develops a novel q-deformation of Brownian motion, connecting algebraic deformations to stochastic process properties.
Findings
q-deformed Brownian motion is non-Gaussian
Cumulant structure of q-deformed process is characterized
Extension of algebraic deformation to stochastic processes
Abstract
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
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