Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces
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 …
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 …
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 …
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 …
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 …
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
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 …
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 …
continuous process which satisfies a linear integral inequality with an added continuous …
Generalized couplings and ergodic rates for SPDEs and other Markov models
We establish verifiable general sufficient conditions for exponential or subexponential
ergodicity of Markov processes that may lack the strong Feller property. We apply the …
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
Spatially structured neural networks driven by jump diffusion noise with monotone
coefficients, fully path dependent delay and with a disorder parameter are considered. Well …
coefficients, fully path dependent delay and with a disorder parameter are considered. Well …
Stability in distribution of stochastic functional differential equations
In this paper we investigate the stability in distribution for a class of stochastic functional
differential equations (SFDEs), which include stochastic differential delay equations …
differential equations (SFDEs), which include stochastic differential delay equations …