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JOURNALS // Teoriya Veroyatnostei i ee Primeneniya // Archive

Teor. Veroyatnost. i Primenen., 1999 Volume 44, Issue 1, Pages 211–225 (Mi tvp618)

This article is cited in 5 papers

Short Communications

An example of large deviations for a stationary process

O. V. Gulinskya, R. Sh. Liptserb

a Institute for Problems of Information Transmission, Moscow
b Department of Electrical Engineering-Systems, Tel Aviv University, Israel

Abstract: We give an example of large deviations for a family $(X_t^\varepsilon)_{t\ge 0}$, $\varepsilon >0$, with $\dot{X}_t^\varepsilon=a(X_t^\varepsilon)+b(X_t^\varepsilon) \eta_{t/\varepsilon}$, where $\eta_t$ is a stationary process obeying the Wold decomposition: $\eta_t=\int_{-\infty}^th(t-s)\,dN_s$ with respect to a homogeneous process $N_t$ with independent square integrable increments.

Keywords: large deviation, Skorokhod space, Wold decomposition.

Language: English

DOI: 10.4213/tvp618


 English version:
Theory of Probability and its Applications, 2000, 44:1, 201–217

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