Results 41 to 50 of about 144 (141)
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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On a semilinear mixed fractional heat equation driven by fractional Brownian sheet [PDF]
, 2017 In this paper, we consider the stochastic heat equation of the form \u2202 u
Xia, Dengfeng +3 more
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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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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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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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HIGH ORDER PARACONTROLLED CALCULUS
Forum of Mathematics, Sigma, 2019 We develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm a whole class of singular partial differential equations with the same efficiency as regularity structures.
ISMAËL BAILLEUL, FRÉDÉRIC BERNICOT
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A non‐nonstandard proof of Reimers′ existence result for heat SPDEs
International Journal of Stochastic Analysis, Volume 11, Issue 1, Page 29-41, 1998., 1997 In 1989, Reimers gave a nonstandard proof of the existence of a solution to heat SPDEs, driven by space‐time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non‐nonstandard proof of this fact, and with the aid of Girsanov′s theorem for continuous ...
Hassan Allouba
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Forum of Mathematics, Pi, 2019 In last passage percolation models lying in the Kardar–Parisi–Zhang (KPZ) universality class, the energy of long energy-maximizing paths may be studied as a function of the paths’ pair of endpoint locations.
ALAN HAMMOND
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Stability of stationary and periodic solutions equations in Banach space
International Journal of Stochastic Analysis, Volume 10, Issue 3, Page 249-255, 1997., 1997 Linear difference and differential equations with operator coefficients and random stationary (periodic) input are considered. Conditions are presented for the mean stability of stationary (periodic) solutions under small perturbation of the coefficients.
A. Ya. Dorogovtsev
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On large deviations regimes for random media models [PDF]
, 2006 We investigate the behavior of probabilities of large deviations above the mean versus large deviations below the mean for random additive functionals in a variety of random media models.
Gauthier, Damien
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