Large deviations for (1 + 1)-dimensional stochastic geometric wave equation

Autor: Zdzisław Brzeźniak, Ben Gołdys, Martin Ondreját, Nimit Rana

Publikováno v: Journal of Differential Equations. 325:1-69

We consider stochastic wave map equation on real line with solutions taking values in a $d$-dimensional compact Riemannian manifold. We show first that this equation has unique, global, strong in PDE sense, solution in local Sobolev spaces. The main

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7cfe82f488c07774beadf9d63866c13a
https://doi.org/10.1016/j.jde.2022.04.003

Numerical approximation of nonlinear SPDE’s

Autor: Martin Ondreját, Andreas Prohl, Noel J. Walkington

Publikováno v: Stochastics and Partial Differential Equations: Analysis and Computations.

The numerical analysis of stochastic parabolic partial differential equations of the form $$\begin{aligned} du + A(u)\, dt = f \,dt + g \, dW, \end{aligned}$$ d u + A ( u ) d t = f d t + g d W , is surveyed, where A is a nonlinear partial operator an

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b9090f3e4b28dcbe0a2e2d4caaf39ad2
https://doi.org/10.1007/s40072-022-00271-9

On temporal regularity of stochastic convolutions in 2-smooth Banach spaces

Autor: Mark Veraar, Martin Ondreját

Publikováno v: Annales de l'Institut Henri Poincar. (B) Probabilites et Statistiques, 56(3)
Ann. Inst. H. Poincaré Probab. Statist. 56, no. 3 (2020), 1792-1808

We show that paths of solutions to parabolic stochastic differential equations have the same regularity in time as the Wiener process (as of the current state of art). The temporal regularity is considered in the Besov-Orlicz space $B^{1/2}_{\Phi_2,\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::076114bca4dddf2a84771d01b724ec04
http://resolver.tudelft.nl/uuid:a1d7ea36-68cc-4bc9-b19d-730628000028

Uniqueness of the nonlinear Schrödinger equation driven by jump processes

Autor: Martin Ondreját, Erika Hausenblas, Anne de Bouard

Publikováno v: Nonlinear Differential Equations and Applications
Nonlinear Differential Equations and Applications, Springer Verlag, 2019, 26 (3), ⟨10.1007/s00030-019-0569-3⟩

In a recent paper by the first two authors, existence of martingale solutions to a stochastic nonlinear Schrodinger equation driven by a Levy noise was proved. In this paper, we prove pathwise uniqueness, uniqueness in law and existence of strong sol

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::769c3cd668ccb82e44bcc2dcc807ed24
https://hal.archives-ouvertes.fr/hal-02388375

$L^p$-valued stochastic convolution integral driven by Volterra noise

Autor: Bohdan Maslowski, Petr Čoupek, Martin Ondreját

Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space $L^p$. The corresponding regularity is obtained by showing that the stochastic convolution integrals ar

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::daf07c5f2e0bdba8c20a2d2acee1c76f
http://arxiv.org/abs/1704.03307