The Kolmogorov infinite dimensional equation in a Hilbert space via deep learning methods

J Castro - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
We consider the nonlinear Kolmogorov equation posed in a Hilbert space H, not necessarily
of finite dimension. This model was recently studied by Cox et al.[12] in the framework of …

SPDEs driven by standard symmetric α-stable cylindrical Lévy processes: Existence, Lyapunov functionals and Itô formula

G Bodó, M Riedle, O Týbl - Electronic Journal of Probability, 2024 - projecteuclid.org
We investigate several aspects of solutions to stochastic evolution equations in Hilbert
spaces driven by a standard symmetric α-stable cylindrical noise. Similarly to cylindrical …

On a class of stochastic partial differential equations with multiple invariant measures

B Farkas, M Friesen, B Rüdiger, D Schroers - … Differential Equations and …, 2021 - Springer
In this work we investigate the long-time behavior for Markov processes obtained as the
unique mild solution to stochastic partial differential equations in a Hilbert space. We …

Markovian Lifts of Stochastic Volterra Equations in Sobolev Spaces: Solution theory, an Ito Formula and Invariant Measures

F Huber - arXiv preprint arXiv:2406.10352, 2024 - arxiv.org
We investigate Markovian lifts of stochastic Volterra equations (SVEs) with completely
monotone kernels and general coefficients within a class of weighted Sobolev spaces. Our …

SPDEs driven by standard symmetric -stable cylindrical L\'evy processes: existence, Lyapunov functionals and It\^{o} formula

G Bodó, O Týbl, M Riedle - arXiv preprint arXiv:2402.01211, 2024 - arxiv.org
We investigate several aspects of solutions to stochastic evolution equations in Hilbert
spaces driven by a standard symmetric $\alpha $-stable cylindrical noise. Similarly to …

Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises

X Yang, W Zhao - Applied Mathematics and Computation, 2018 - Elsevier
In this paper, we investigate the mean square error of numerical methods for SPDEs driven
by Gaussian and non-Gaussian noises. The Gaussian noise considered here is a Hilbert …

Stability properties of mild solutions of SPDEs related to pseudo differential equations

V Mandrekar, B Rüdiger - … Physics: Sergio Albeverio, Adventures of a …, 2023 - Springer
This is a review article which presents part of the contribution of Sergio Albeverio to the
study of existence and uniqueness of solutions of SPDEs driven by jump processes and …

Existence, regularity, and a strong itô formula for the isochronal phase of spde

ZP Adams - Electronic Communications in Probability, 2024 - projecteuclid.org
We prove the existence and regularity of the isochron map for stable invariant manifolds of a
large class of evolution equations. Our results apply in particular to the isochron map of …

[PDF][PDF] Stochastic Analysis for Cylindrical Lévy Processes

G Bodó - 2023 - kclpure.kcl.ac.uk
The purpose of this thesis is to lay down the theoretical foundations necessary for the
successful application of cylindrical Lévy processes as models of random perturbations of …

[PDF][PDF] On a class of stochastic partial differential equations with multiple invariant measures

B Farkas, M Friesen, B Rüdiger, D Schroers - 2020 - imacm.uni-wuppertal.de
In this work we investigate the long-time behavior for Markov processes obtained as the
unique mild solution to stochastic partial differential equations in a Hilbert space. We …