Karhunen-Loève expansions of α-Wiener bridges

• Autorzy: Mátyás Barczy , Endre Iglói
• Języki publikacji: EN

Abstrakty

EN

We study Karhunen-Loève expansions of the process(X t(α))t∈[0,T) given by the stochastic differential equation $$ dX_t^{(\alpha )} = - \frac{\alpha } {{T - t}}X_t^{(\alpha )} dt + dB_t ,t \in [0,T) $$, with the initial condition X 0(α) = 0, where α > 0, T ∈ (0, ∞), and (B t)t≥0 is a standard Wiener process. This process is called an α-Wiener bridge or a scaled Brownian bridge, and in the special case of α = 1 the usual Wiener bridge. We present weighted and unweighted Karhunen-Loève expansions of X (α). As applications, we calculate the Laplace transform and the distribution function of the L 2[0, T]-norm square of X (α) studying also its asymptotic behavior (large and small deviation).

Słowa kluczowe

EN

α-Wiener bridge; Scaled Brownian bridge; Karhunen-Loève expansion; Laplace transform; Large deviation; Small deviation

Kategorie tematyczne

• 60G15: Gaussian processes
• 60F10: Large deviations
• 60G12: General second-order processes

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 1
• Strony: 65-84

Daty

wydano

2011-02-01

online

2010-12-30

Twórcy

autor

Mátyás Barczy

• University of Debrecen

autor

Endre Iglói

• University of Debrecen

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Identyfikatory

DOI

10.2478/s11533-010-0090-8