Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces

A Singh, A Shukla, V Vijayakumar… - Chaos, Solitons & …, 2021 - Elsevier
In this article, we discuss the asymptotic stability and mean square stability of stochastic
differential equations of fractional-order 1< α≤ 2. We have considered the family of …

[HTML][HTML] Distribution dependent SDEs with singular coefficients

X Huang, FY Wang - Stochastic Processes and their Applications, 2019 - Elsevier
Under integrability conditions on distribution dependent coefficients, existence and
uniqueness are proved for distribution dependent SDEs with non-degenerate noise. When …

[BOOK][B] Harnack inequalities for stochastic partial differential equations

FY Wang - 2013 - Springer
The key point of Harnack's inequality is to compare values at two different points for positive
solutions of a partial differential equation. This inequality was introduced by Harnack [21] in …

Subgeometric rates of convergence of Markov processes in the Wasserstein metric

O Butkovsky - 2014 - projecteuclid.org
We establish subgeometric bounds on convergence rate of general Markov processes in the
Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition …

Non-ergodic delocalization in the Rosenzweig–Porter model

P von Soosten, S Warzel - Letters in Mathematical Physics, 2019 - Springer
Abstract We consider the Rosenzweig–Porter model H= V+ T\,\varPhi H= V+ T Φ, where V is
a N * NN× N diagonal matrix,\varPhi Φ is drawn from the N * NN× N Gaussian Orthogonal …

On existence and continuity results of solution for multi-time scale fractional stochastic differential equation

A Alkhazzan, J Wang, C Tunç, X Ding, Z Yuan… - Qualitative Theory of …, 2023 - Springer
In this paper, we study four critical aspects of a new class of multi-time scale nonlinear
fractional stochastic differential equations with fractional integral in the sense of Riemann …

A stochastic Gronwall lemma

M Scheutzow - … Analysis, Quantum Probability and Related Topics, 2013 - World Scientific
We prove a stochastic Gronwall lemma of the following type: if Z is an adapted non-negative
continuous process which satisfies a linear integral inequality with an added continuous …

Generalized couplings and ergodic rates for SPDEs and other Markov models

O Butkovsky, A Kulik, M Scheutzow - The Annals of Applied Probability, 2020 - JSTOR
We establish verifiable general sufficient conditions for exponential or subexponential
ergodicity of Markov processes that may lack the strong Feller property. We apply the …

Propagation of chaos for stochastic spatially structured neuronal networks with delay driven by jump diffusions

S Mehri, M Scheutzow, W Stannat… - The Annals of Applied …, 2020 - JSTOR
Spatially structured neural networks driven by jump diffusion noise with monotone
coefficients, fully path dependent delay and with a disorder parameter are considered. Well …

Stability in distribution of stochastic functional differential equations

Y Wang, F Wu, X Mao - Systems & Control Letters, 2019 - Elsevier
In this paper we investigate the stability in distribution for a class of stochastic functional
differential equations (SFDEs), which include stochastic differential delay equations …