• Publications
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On the support of solutions to the heat equation with noise
Let be 2-parameter white noise. Let satisfy and suppose that is bounded, nonnegative, with compact support and not identically 0. We show that with probability for all . This complements results ofExpand
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Some Non-Linear S.P.D.E's That Are Second Order In Time
• Mathematics
• 1 July 2002
We extend J.B. Walsh's theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,Expand
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• PDF
The Length of the Longest Increasing Subsequence of a Random Mallows Permutation
• Mathematics, Physics
• 16 February 2011
The Mallows measure on the symmetric group Sn is the probability measure such that each permutation has probability proportional to q raised to the power of the number of inversions, where q is aExpand
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• PDF
Regularity of the density for the stochastic heat equation
• Mathematics
• 17 September 2007
We study the smoothness of the density of a semilinear heat equation with multiplicative spacetime white noise. Using Malliavin calculus, we reduce the problem to a question of negative moments ofExpand
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Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality
• Mathematics, Physics
• 1 July 2003
The stochastic Fisher–Kolmogorov–Petrovsky–Piscunov equation is∂tU(x,t)=D∂xxU+γU(1−U)+eU(1−U)η(x,t)for 0⩽U⩽1 where η(x,t) is a Gaussian white noise process in space and time. Here D, γ and e areExpand
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Long time existence for the wave equation with a noise term
We consider the equationut=uxx+uγ W forx on a finite interval, with Dirichlet boundary conditions. W is spacetime white noise. The initial condition is continuous and nonnegative. We show existenceExpand
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The compact support property for solutions to the heat equation with noise
• Mathematics
• 1 September 1992
SummaryWe consider all solutions of a martingale problem associated with the stochastic pde $$u_t = \tfrac{1}{2}u_{xx} + u^\gamma \dot W$$ and show thatu(t,·) has compact support for allt≧0 ifu(0,·)Expand
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Intermittency properties in a hyperbolic Anderson problem
• Mathematics
• 1 November 2009
Keywords: Stochastic wave equation ; Stochastic partial differential equations ; Moment Lyapunov exponents ; Intermittency ; Stochastic heat equation ; Stochastic Wave-Equation ; Model ; DimensionsExpand
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Impact of newly diagnosed abnormal glucose regulation on long-term prognosis in low risk patients with ST-elevation myocardial infarction: A follow-up study
BackgroundPatients with acute myocardial infarction and newly detected abnormal glucose regulation have been shown to have a less favourable prognosis compared to patients with normal glucoseExpand
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