Coupling for some partial differential equations driven by white noise [PDF]
arXiv, 2004 We prove, using coupling arguments, exponential convergence to equilibrium for reaction--diffusion and Burgers equations driven by space-time white noise. We use a coupling by reflection.
arxiv
On random measures on the space of trajectories and strong and weak solutions of stochastic equations [PDF]
Ukrainian Mathematical Journal, 2004, #5, 2005 The random measures on the space of continuous functions are considered. Stationary random measures are described. The weak solutions of the stochastic equations are substituted by the strong measure-valued solutions.
arxiv
Large Deviations for Stochastic Generalized Porous Media Equations [PDF]
arXiv, 2005 The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.
arxiv
Early warning signs for SPDEs with continuous spectrum
European Journal of Applied MathematicsIn this work, we study early warning signs for stochastic partial differential equations (SPDEs), where the linearisation around a steady state is characterised by continuous spectrum. The studied warning sign takes the form of qualitative changes in the
Paolo Bernuzzi +2 more
doaj +1 more source
Maximum principle for SPDEs and its applications [PDF]
arXiv, 2006 The maximum principle for SPDEs is established in multidimensional $C^{1}$ domains. An application is given to proving the H\"older continuity up to the boundary of solutions of one-dimensional SPDEs.
arxiv
Small noise asymptotic of the timing jitter in soliton transmission [PDF]
arXiv, 2006 This submission has been withdrawn because it is a duplicate of [math.PR/0609434].
arxiv
One Brownian Stochastic Flow [PDF]
Theory of Stochastic Processes.- Vol.10 (26), no. 3-4, 2004, pp.
21-25, 2006 The weak limits of the measure-valued processes organized as a mass carried by the interacting Brownian particles are described. As a limiting flow the Arrattia flow is obtained.
arxiv
Effects of aging and hydrothermal treatment on the crystallization of ZSM-5 zeolite synthesis from bentonite. [PDF]
RSC Adv, 2023 Nguyen DK +5 more
europepmc +1 more source
A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise [PDF]
arXiv, 2007 A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation.
arxiv
A Khasminskii type averaging principle for stochastic reaction-diffusion equations [PDF]
arXiv, 2008 We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite dimensional systems.
arxiv