Zobrazeno 1 - 10
of 77
pro vyhledávání: '"Dareiotis, Konstantinos"'
We consider the stochastic reaction-diffusion equation in $1+1$ dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-H\"older space with any regularity index larger than $-1$. We assume that the
Externí odkaz:
http://arxiv.org/abs/2409.11130
The goal of this article is to establish a central limit theorem for the Euler-Maruyama scheme approximating multidimensional SDEs with elliptic Brownian diffusion, under very mild regularity requirements on the drift coefficients. When the drift is
Externí odkaz:
http://arxiv.org/abs/2309.16339
The stochastic thin-film equation with mobility exponent $n\in [\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich noise is considered. We show that martingale solutions exist for non-negative initial values. This advances
Externí odkaz:
http://arxiv.org/abs/2305.06017
Publikováno v:
Ann. Probab. 52 (5), 1864-1902, (2024)
Differential equations perturbed by multiplicative fractional Brownian motions are considered. Depending on the value of the Hurst parameter $H$, the resulting equation is pathwise viewed as an ODE, YDE, or RDE. In all three regimes we show regularis
Externí odkaz:
http://arxiv.org/abs/2207.03476
We study the strong rate of convergence of the Euler--Maruyama scheme for a multidimensional stochastic differential equation (SDE) $$ dX_t = b(X_t) \, dt + dL_t, $$ with irregular $\beta$-H\"older drift, $\beta > 0$, driven by a L\'evy process with
Externí odkaz:
http://arxiv.org/abs/2204.12926
Publikováno v:
SIAM Journal on Numerical Analysis, Volume 61, 1103 - 1137 (2023)
A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the non-linear re
Externí odkaz:
http://arxiv.org/abs/2110.06148
Publikováno v:
Ann. Appl. Probab. 33(3): 2291-2323 (2023)
We derive sharp strong convergence rates for the Euler-Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on the drift coefficient. In case the noise is additive, we show that Sobol
Externí odkaz:
http://arxiv.org/abs/2101.12185
Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
Publikováno v:
Arch. Rational Mech. Anal. 242(1) 179-234 (2021)
We prove the existence of nonnegative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites
Externí odkaz:
http://arxiv.org/abs/2012.04356
Publikováno v:
Ann. Inst. H. Poincar\'e Probab. Statist. 57(4): 2354-2371 (2021)
The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space-time white noise is established in spatial dimension one. The Stroock-Varopoulos inequality is identified as a key tool in the deriva
Externí odkaz:
http://arxiv.org/abs/2002.12924
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