Gaussian noise related to generalised Ehrenfest model

Y. Miniailyk
Theory of Stochastic Processes
Vol.26 (42), no.1, 2022, pp.21-26
In this article we consider the generalization of Ehrenfest model, where at each moment of time not 1 but some k of n particles go from one box to another. We describe this process by a sequence of Bernoulli random vectors. We define related Bernoulli noise on a set of continuous functions for different times, and prove that it converges to Ornstein-Uhlenbeck sequence of Gaussian white noises when number of particles tends to infinity.
DOI: https://doi.org/10.37863/tsp-0919442573-40
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