We give a new representation of fractional Brownian motion with Hurst parameter H
A Feynman-Kac-type formula for the deterministic and stochastic wave equations (2007)
Dalang, Robert C., Mueller, Carl, Tribe, Roger
We establish a probabilistic representation for a wide class of linear deterministic p.d.e.s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies...
Regularity of the density for the stochastic heat equation (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 of...
Fleischmann, Klaus, Mueller, Carl, Vogt, Pascal
In a recent work, Fleischmann and Mueller (2004) showed the existence of a super-Brownian motion in R^d, d=2,3, with extra birth at the origin. Their construction made use of an analytical approach...
Some properties for superprocess under a stochastic flow (2006)
Lee, Kijung, Mueller, Carl, Xiong, Jei
For a superprocess under a stochastic flow, we prove that it has a density with respect to the Lebesgue measure for d=1 and is singular for d>1. For d=1, a stochastic partial differential equation is...
The heat equation with multiplicative stable L\'evy noise (2005)
Mueller, Carl, Mytnik, Leonid, Stan, Aurel
We study the heat equation with a random potential term. The potential is a one-sided stable noise, with positive jumps, which does not depend on time. To avoid singularities, we define the equation...
Some Non-Linear S.P.D.E's That Are Second Order In Time (2003)
Dalang, Robert C.; Ecole Polytechnique Fédérale; Robert.dalang@epfl.ch, Mueller, Carl; University Of Rochester; Cmlr@math.rochester.edu
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,...
Super-Brownian motion with extra birth at one point (2002)
Fleischmann, Klaus, Mueller, Carl
A super-Brownian motion in two and three dimensions is constructed where ``particles'' give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based...
Some non-linear s.p.d.e.'s that are second order in time (2002)
Dalang, Robert C., Mueller, Carl
We extend Walsh's theory of martingale measures in order to deal with hyperbolic stochastic partial differential equations that are second order in time, such as the wave equation and the beam...
Hitting Properties of a Random String (2002)
Mueller, Carl; University Of Rochester; Cmlr@math.rochester.edu, Tribe, Roger; University Of Warwick; Tribe@maths.warwick.ac.uk
We consider Funaki's model of a random string taking values in Rd. It is specified by the following stochastic PDE, ut = uxx + W where W=W(x,t) is two-parameter white noise, also taking values in...
A Singular Parabolic Anderson Model (2002)
We give a new example of a measure-valued process without a density, which arises from a stochastic partial differential equation with a multiplicative noise term. This process has some unusual...
Hitting properties of a random string (2001)
We consider Funaki's model of a random string taking values in R^d. It is specified by the following stochastic PDE, du = u_{xx} + W, where W=W(x,t) is two-parameter white noise, also taking values...
The critical parameter for the heat equation with a noise term to blow up in finite time (2000)
Consider the stochastic partial differential equation $u_t=u_{xx}+u^\gammaW$ where $x\in\mathbf{I}\equiv[0,J], W=W(t,x)$ is 2-parameter white noise, and we assume that the initial function $u(0,x)$...
Finite time extinction of superprocesses with catalysts (2000)
Dawson, Donald A., Fleischmann, Klaus, Mueller, Carl
Consider a catalytic super-Brownian motion $X =X^\Gamma$ with finite variance branching. Here “catalytic ” means that branching of the reactant $X$ is only possible in the presence of some...
The sort-first architecture for real-time image generation / (2000)
Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2000.
Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2000.
The Critical Parameter for the Heat Equation with a Noise Term to Blow Up in Finite Time (1999)
Consider the stochastic partial differential equation u_t=u_{xx}+u^gamma dot{W}, where x in [0,J], dot{W}=dot{W}(t,x) is 2-parameter white noise, and we assume that the initial function u(0,x) is...
A Distributed Implementation of an N-body Virtual World Simulation (1998)
Mark Parris, Carl Mueller, Jan Prins, Adam Duggan, Quan Zhou, Erik Erikson
Meeting the challenge of real-time visualization of a complex physical simulation can require several specialized computers. The virtual-world simulation described in this paper combines a...
Finite time extinction of super-Brownian motions with catalysts (1998)
Dawson, Donald A., Fleischmann, Klaus, Mueller, Carl
Consider a catalytic super-Brownian motion $X=X^\Gamma$ with finite variance branching. Here `catalytic' means that branching of the reactant $X$ is only possible in the presence of some catalyst....
Finite Width For a Random Stationary Interface (1997)
Mueller, Carl; University Of Rochester; Cmlr@math.rochester.edu, Tribe, Roger; University Of Warwick; Tribe@maths.warwick.ac.uk
We study the asymptotic shape of the solution $u(t,x) in [0,1]$ to a one-dimensional heat equation with a multiplicative white noise term. At time zero the solution is an interface, that is $u(0,x)$...
Hierarchical Graphics Databases in Sort-First (1997)
Sort-first architectures for parallel rendering use the natural frame-to-frame coherence of primitives on the screen to increase performance by grouping primitives that are close together on the...
Long time existence for the wave equation with a noise term (1997)
.1 2 We consider the equation $u_{tt} = \Delta u + a(u) \mathsf{N}$ for $x \epsilon \mathbf{R}^1$ or $R^2$. $\mathsf{N}$ is a Gaussian noise term, which is white noise if $x \epsilon \mathbf{R}^1$....
Singular initial conditions for the heat equation with a noise term (1996)
We consider the equation $$\begin{array}{r@{=}l}u_t \, =\, u_{xx}+ u^\gamma\dot{W}, \quad t>0, \; 0\leq x \leq J,\\[1ex]u(0, x) \, =\, u_0 (x),\\[1ex]u(t, 0) \, = \, u(t, J) =0,\end{array}$$ where...
Blowup For The Heat Equation With A Noise Term (1995)
In this paper we study blowup of the equation u t = u xx + u fl W tx , where W tx is a two-dimensional white noise field and where Dirichlet boundary conditions are enforced. It is known that if fl !...
The Sort-First Rendering Architecture for High-Performance Graphics (1995)
Interactive graphics applications have long been challenging graphics system designers by demanding machines that can provide ever increasing polygon rendering performance. Another trend in...
A Distributed Implementation of an N-body Virtual World Simulation (1995)
Mark Parris, Carl Mueller, Jan Prins, Adam Duggan, Quan Zhou, Erik Erikson
Meeting the challenge of real-time visualization of a complex physical simulation can require several specialized computers. The virtual-world simulation described in this paper combines a...
A Distributed Implementation of an N-body Virtual World Simulation (1995)
Mark Parris, Carl Mueller, Jan Prins, Adam Duggan, Quan Zhou, Erik Erikson
Meeting the challenge of real-time visualization of a complex physical simulation can require several specialized computers. The virtual-world simulation described in this paper combines a...
A Distributed Implementation of an N-body Virtual World Simulation (1995)
Mark Parris, Carl Mueller, Jan Prins, Adam Duggan, Quan Zhou, Erik Erikson
Meeting the challenge of real-time visualization of a complex physical simulation can require several specialized computers. The virtual-world simulation described in this paper combines a...