Representation of stationary and stationary increment processes via Langevin equation and self-similar processes

Lauri Viitasaari

Statistics & Probability Letters, 2016, vol. 115, issue C, 45-53

Abstract: Let Wt be a standard Brownian motion. It is well-known that the Langevin equation dUt=−θUtdt+dWt defines a stationary process called Ornstein–Uhlenbeck process. Furthermore, Langevin equation can be used to construct other stationary processes by replacing Brownian motion Wt with some other process G with stationary increments. In this article we prove that the converse also holds and all continuous stationary processes arise from a Langevin equation with certain noise G=Gθ. Discrete analogies of our results are given and applications are discussed.

Keywords: Stationary processes; Stationary increment processes; Self-similar processes; Lamperti transform; Langevin equation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2016.03.020

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