G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics

Details G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion in Quantum Mechanics

2011-05-05

arxiv.org/abs/1105.1055v1

Mathematics

Probability

Scientific paper

We provide a general approach to construct a stochastic process with a given consistent family of finite dimensional distributions under a nonlinear expectation space. We use this approach to construct a generalized Gaussian process under a sublinear expectation and a q-Brownian motion. The later one is under a complex-valued linear expectation, with which a new type of Feynman-Kac formula can be derived to represent the solution of a Schr\"odinger equation.

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