Displaying similar documents to “Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise*”

Lp-theory for the stochastic heat equation with infinite-dimensional fractional noise

Raluca M. Balan (2011)

ESAIM: Probability and Statistics

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In this article, we consider the stochastic heat equation d u = ( Δ u + f ( t , x ) ) d t + ∑ k = 1 ∞ g k ( t , x ) δ β t k , t ∈ [ 0 , T ] , with random coefficients and , driven by a sequence () of i.i.d. fractional Brownian motions of index . Using the Malliavin calculus techniques and a -th moment maximal inequality for the infinite sum of Skorohod integrals with respect to (), we prove that the equation has a unique solution (in a Banach space of summability exponent ≥ 2), and this solution is Hölder continuous in both time and space.

Periodicity of -expansions for certain Pisot units

Sandra Vaz, Pedro Martins Rodrigues (2012)

ESAIM: Proceedings

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Given β > 1, let T β T β : [ 0 , 1 [ → [ 0 , 1 [ x → βx − ⌊ βx ⌋ . The iteration of this transformation gives rise to the greedy β-expansion. There has been extensive research on the properties of this expansion and its dependence on the parameter β. ...

Limit theorems for measure-valued processes of the level-exceedance type

Andriy Yurachkivsky (2012)

ESAIM: Probability and Statistics

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Let, for each , (, ۔) be a random measure on the Borel -algebra in ℝ such that E(, ℝ) < ∞ for all and let ψ ^ (, ۔) be its characteristic function. We call the function ψ ^ ( ,…, ; ,…, ) = 𝖤 ∏ j = 1 l ψ ^ ( t j , z j ) of arguments ℕ, , … , , ℝ the of the measure-valued random function (MVRF) (۔, ۔). A...

Stabilité sous condition CFL non linéaire

Erwan Deriaz, Dmitry Kolomenskiy (2012)

ESAIM: Proceedings

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We present a basic althought little known numerical stability condition: for convection equations, the von Neumann stability constraint ∥ ∥ ≤ (1 +    Δ) ∥ ∥ drives to the stability condition Δ ≤ Δ with α = p ( 2 q − 1 ) q ( 2 p − 1 ) where is an integer linked to the stability domain of the time scheme and  ≥  an integer linked to the upwind property of the space discretization...