Abstract
An important observation of this paper is that a non-trivial $ G $-Brownian motion is not a Gaussian process, e.g., finite dimensional distributions of $ G $-Brownian motion is not G-normal, or G-Gaussian. We then have to start from the very beginning, to establish the foundation of $ G $-Gaussian processes which is more suitable for space-parameter systems. It is known that the notion of classical Brownian motion is not suitable to model the random propagation of a quantum particle. In this paper we have rigorously defined a new stochastic process called $ q $-Brownian who's propagator exactly coincides with the one proposed by Feynman based on the solution of Schrödinger equation. The notion of expectation plays a fundamental base of the above results. This paper was originally published on [38].
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.