Constructing stationary Gaussian processes from deterministic processes with random initial conditions
2002-06
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Constructing stationary Gaussian processes from deterministic processes with random initial conditions
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2002-06
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We consider a family of stationary Gaussian processes that includes the stationary Ornstein-Uhlenbeck process. We show that processes in this family can be attained as the limit of a sequence of deterministic processes with random initial conditions. Weak convergence in the supremum norm on finite time-intervals is shown. We also establish the convergence of a wide variety of long-term statistics. Our construction provides a rigorous example of how macroscopic stochastic dynamics can be derived from microscopic deterministic dynamics.
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Tupper, P.F.. (2002). Constructing stationary Gaussian processes from deterministic processes with random initial conditions. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3776.
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