Results 21 to 30 of about 134 (133)
International Journal of Stochastic Analysis, Volume 2004, Issue 2, Page 109-122, 2004., 2004 This paper is concerned with the study of the rate of convergence of the distribution of the maximum likelihood estimator of a parameter appearing linearly in the drift coefficients of two types of stochastic partial differential equations (SPDEs).
M. N. Mishra, B. L. S. Prakasa Rao
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On a stochastic Burgers equation with Dirichlet boundary conditions
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 43, Page 2735-2746, 2003., 2003 We consider the one‐dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non‐Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Ekaterina T. Kolkovska
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Stochastic flows with interaction and measure‐valued processes
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 63, Page 3963-3977, 2003., 2003 We consider the new class of the Markov measure‐valued stochastic processes with constant mass. We give the construction of such processes with the family of the probabilities which describe the motion of single particles. We also consider examples related to stochastic flows with the interactions and the local times for such processes.
Andrey A. Dorogovtsev
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A Haussmann‐Clark‐Ocone formula for functionals of diffusion processes with Lipschitz coefficients
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 357-370, 2002., 2002 We establish a martingale representation formula for functionals of diffusion processes with Lipschitz coefficients, as stochastic integrals with respect to the Brownian motion.
Khaled Bahlali +2 more
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Ergodicity of stochastically forced large scale geophysical flows
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 6, Page 313-320, 2001., 2001 We investigate the ergodicity of 2D large scale quasigeostrophic flows under random wind forcing. We show that the quasigeostrophic flows are ergodic under suitable conditions on the random forcing and on the fluid domain, and under no restrictions on viscosity, Ekman constant or Coriolis parameter.
Jinqiao Duan, Beniamin Goldys
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PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
Forum of Mathematics, Pi, 2015 We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths.
MASSIMILIANO GUBINELLI +2 more
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On the stability of stationary solutions of a linear integro‐differential equation
International Journal of Stochastic Analysis, Volume 14, Issue 2, Page 139-150, 2001., 2001 In this paper the following two connected problems are discussed. The problem of the existence of a stationary solution for the abstract equation εx"(t)+x′(t)=Ax(t)+∫−∞tE(t−s)x(s)ds+ξ(t),t∈R containing a small parameter ε in Banach space B is considered. Here A ∈ ℒ(B) is a fixed operator, E ∈ C([0, +∞), ℒ(B)) and ξ is a stationary process.
A. Ya. Dorogovtsev, O. Yu. Trofimchuk
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Galerkin approximation and the strong solution of the Navier‐Stokes equation
International Journal of Stochastic Analysis, Volume 13, Issue 3, Page 239-259, 2000., 2000 We consider a stochastic equation of Navier‐Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Hannelore Breckner
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Periodic in distribution solution for a telegraph equation
International Journal of Stochastic Analysis, Volume 12, Issue 2, Page 121-131, 1999., 1998 In this paper we study an abstract stochastic equation of second order and stochastic boundary problem for the telegraph equation in a strip. We prove the existence of solutions, which are d‐periodic (periodic in distribution) random processes.
A. Ya. Dorogovtsev
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A CLASS OF GROWTH MODELS RESCALING TO KPZ
Forum of Mathematics, Pi, 2018 We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf–Cole solutions to the KPZ equation.
MARTIN HAIRER, JEREMY QUASTEL
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