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14
Pathwise Uniqueness for Stochastic Heat Equations with Hölder Continuous Coefficients: the White Noise Case
, 2009
"... Abstract. We prove pathwise uniqueness for solutions of parabolic stochastic pde’s with multiplicative white noise if the coefficient is Hölder continuous of index γ> 3/4. The method of proof is an infinitedimensional version of the YamadaWatanabe argument for ordinary stochastic differential e ..."
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Cited by 18 (7 self)
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Abstract. We prove pathwise uniqueness for solutions of parabolic stochastic pde’s with multiplicative white noise if the coefficient is Hölder continuous of index γ> 3/4. The method of proof is an infinitedimensional version of the YamadaWatanabe argument for ordinary stochastic differential equations.
Effect of noise on front propagation in reactiondiffusion equations of KPP type. Preprint, available at arXiv:0902.3423
"... We consider reactiondiffusion equations of KPP type in one spatial dimension, perturbed by a FisherWright white noise, under the assumption of uniqueness in distribution. Examples include the randomly perturbed FisherKPP equations and ∂tu = ∂ 2 xu + u(1 − u) + ǫ p u(1 − u) ˙ W, (0.1) ∂tu = ∂ 2 ..."
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Cited by 16 (3 self)
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We consider reactiondiffusion equations of KPP type in one spatial dimension, perturbed by a FisherWright white noise, under the assumption of uniqueness in distribution. Examples include the randomly perturbed FisherKPP equations and ∂tu = ∂ 2 xu + u(1 − u) + ǫ p u(1 − u) ˙ W, (0.1) ∂tu = ∂ 2 xu + u(1 − u) + ǫ √ u ˙ W, (0.2) where ˙ W = ˙ W(t, x) is a spacetime white noise.
An Introduction to U.S
 Telecommunications Law. Artech
, 1994
"... Speed and diversity of evolution in subdivided populations ..."
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Cited by 14 (0 self)
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Speed and diversity of evolution in subdivided populations
NONUNIQUENESS FOR NONNEGATIVE SOLUTIONS OF PARABOLIC STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
"... Abstract. Pathwise nonuniqueness is established for nonnegative solutions of the parabolic stochastic pde ..."
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Cited by 4 (1 self)
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Abstract. Pathwise nonuniqueness is established for nonnegative solutions of the parabolic stochastic pde
Intermittency and aging for the symbiotic branching model
, 2009
"... Abstract. For the symbiotic branching model introduced in (EF04), it is shown that aging and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second mom ..."
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Cited by 4 (1 self)
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Abstract. For the symbiotic branching model introduced in (EF04), it is shown that aging and intermittency exhibit different behaviour for negative, zero, and positive correlations. Our approach also provides an alternative, elementary proof and refinements of classical results concerning second moments of the parabolic Anderson model with Brownian potential. Some refinements to more general (also infinite range) kernels of recent aging results of (DD07) for interacting diffusions are given.
Cluster Formation in a Stepping Stone Model With Continuous, Hierarchically Structured Sites
, 1995
"... A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be understood as a continuum limit of discrete statespace, two allele, genetics models with hierarchically ..."
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Cited by 2 (2 self)
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A stepping stone model with site space a continuous, hierarchical group is constructed via duality with a system of (delayed) coalescing "stable" L'evy processes. This model can be understood as a continuum limit of discrete statespace, two allele, genetics models with hierarchically structured resampling and migration. The existence of a process rescaling limit on suitable large space and time scales is established and interpreted in terms of the dynamics of cluster formation. This paper was inspired by recent work of Klenke. AMS 1980 subject classifications. Primary 60K35; secondary 60J60, 60B15. Key words and phrases. Interacting diffusion, stepping stone model, cluster formation, clustering, coalescing L'evy process, hierarchical structures, resampling, migration. (*) Research supported in part by a Presidential Young Investigator Award and an Alfred P. Sloan Foundation Fellowship 2 S.N. Evans & K. Fleischmann 1 Introduction and results 1.1 Background In several physical and ...
Nonuniqueness for a parabolic SPDE with 3/4 − εHölder Diffusion Coefficients
"... Motivated by Girsanov’s nonuniqueness examples for SDE’s, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) ∂u ..."
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Cited by 1 (1 self)
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Motivated by Girsanov’s nonuniqueness examples for SDE’s, we prove nonuniqueness for the parabolic stochastic partial differential equation (SPDE) ∂u
Fine Properties of Symbiotic Branching Processes vorgelegt von DiplomMathematiker
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Elect. Comm. in Probab. 10 (2005), 136{145 ELECTRONIC COMMUNICATIONS in PROBABILITY ON THE DUALITY BETWEEN COALESCING BROWNIAN PARTICLES AND THE HEAT EQUATION DRIVEN BY FISHERWRIGHT NOISE
, 2005
"... This paper concerns the Markov process duality between the onedimensional heat equation driven by FisherWright white noise and slowly coalescing Brownian particles. A representation is found for the law of the solution x! Ut(x) to the stochastic PDE, at a ¯xed time, in terms of a labelled system o ..."
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This paper concerns the Markov process duality between the onedimensional heat equation driven by FisherWright white noise and slowly coalescing Brownian particles. A representation is found for the law of the solution x! Ut(x) to the stochastic PDE, at a ¯xed time, in terms of a labelled system of such particles.