Results 11 to 20 of about 108,591 (231)
Small ball probabilities, metric entropy and Gaussian rough paths [PDF]
Journal of Mathematical Analysis and Applications, 2022 We study the Small Ball Probabilities (SBPs) of Gaussian rough paths. While many works on rough paths study the Large Deviations Principles (LDPs) for stochastic processes driven by Gaussian rough paths, it is a noticeable gap in the literature that SBPs have not been extended to the rough path framework.
William Salkeld
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Log-level comparison principle for small ball probabilities [PDF]
Statistics & Probability Letters, 2009 We prove a new variant of comparison principle for logarithmic $L_2$-small ball probabilities of Gaussian processes. As an application, we obtain logarithmic small ball asymptotics for some well-known processes with smooth covariances.
Alexander I Nazarov
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Small ball probabilities for the infinite-dimensional Ornstein–Uhlenbeck process in Sobolev spaces [PDF]
Stochastics and Partial Differential Equations: Analysis and Computations, 2016 While small ball, or lower tail, asymptotic for Gaussian measures generated by solutions of stochastic ordinary differential equations is relatively well understood, a lot less is known in the case of stochastic partial differential equations. The paper presents exact logarithmic asymptotics of the small ball probabilities in a scale of Sobolev spaces ...
Sergey Lototsky
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Small ball probabilities for the stochastic heat equation with colored noise
Stochastic Processes and their ApplicationsWe consider the stochastic heat equation on the 1-dimensional torus $\mathbb{T}:=\left[-1,1\right]$ with periodic boundary conditions: $$ \partial_t u(t,x)=\partial^2_x u(t,x)+σ(t,x,u)\dot{F}(t,x),\quad x\in \mathbb{T},t\in\mathbb{R}_+, $$ where $\dot{F}(t,x)$ is a generalized Gaussian noise, which is white in time and colored in space.
Jiaming Chen
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A fractional Brownian field indexed by $L^2$ and a varying Hurst parameter [PDF]
, 2014 Using structures of Abstract Wiener Spaces, we define a fractional Brownian field indexed by a product space $(0,1/2] \times L^2(T,m)$, $(T,m)$ a separable measure space, where the first coordinate corresponds to the Hurst parameter of fractional ...
Richard, Alexandre
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Rates of contraction of posterior distributions based on Gaussian process priors [PDF]
, 2008 We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing kernel Hilbert ...
van der Vaart, A. W., van Zanten, J. H.
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Small ball probabilities for the Slepian Gaussian fields [PDF]
Transactions of the American Mathematical Society, 2006 The d d -dimensional Slepian Gaussian random field { S ( t ) , t ∈ R + d } \{S({\mathbf {t}}), {\mathbf {t}} \in \mathbb {R}_+^d\}
Gao, Fuchang, Li, Wenbo V.
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Small Ball Probability for the Condition Number of Random Matrices [PDF]
, 2020 Some changes according to the Referee's ...
Litvak, Alexander E. +2 more
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Small-Ball Probabilities for the Volume of Random Convex Sets [PDF]
Discrete & Computational Geometry, 2013 The authors prove several interesting small-deviation estimates for the volume of random convex sets in \(\mathbb R^n\). Typical models involve convex hulls or Minkowski sums of line segments generated by independent random points. The random models considered include absolutely continuous probability measures (wrt Lebesgue measure) with bounded ...
Paouris, Grigoris, Pivovarov, Peter
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The harmonic measure of diffusion-limited aggregates including rare events [PDF]
, 2009 We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results ...
Ball R. C. +6 more
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