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2011 | 9 | 1 | 65-84
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Karhunen-Loève expansions of α-Wiener bridges

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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).
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
1
Strony
65-84
Opis fizyczny
Daty
wydano
2011-02-01
online
2010-12-30
Twórcy
autor
Bibliografia
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Typ dokumentu
Bibliografia
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