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Precise small deviations in L 2 of some Gaussian processes appearing in the regression context

100%
Kirichenko A., Nikitin Y.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1674-1686
EN
We find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.
2
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Karhunen-Loève expansions of α-Wiener bridges

100%
Barczy M., Iglói E.
Open Mathematics
|
2011
|
tom 9
|
nr 1
65-84
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).
3
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Characterization of equilibrium measures for critical reversible Nearest Particle Systems

100%
Mountford T., Wu L.
Open Mathematics
|
2008
|
tom 6
|
nr 2
237-261
EN
We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than $$ \frac{{7 + \sqrt {41} }} {2} $$ and obeys some natural regularity conditions.
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