G-Gaussian Processes under Sublinear Expectations and q-Brownian Motion   in Quantum Mechanics
  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. 
Shige Peng
math.PR