[图书][B] Stochastic calculus for fractional Brownian motion and applications

F Biagini, Y Hu, B Øksendal, T Zhang - 2008 - books.google.com
Fractional Brownian motion (fBm) has been widely used to model a number of phenomena
in diverse fields from biology to finance. This huge range of potential applications makes …

[图书][B] Differential equations driven by rough paths

TJ Lyons, M Caruana, T Lévy - 2007 - Springer
In this chapter, we finally make sense of a solution of a differential equation driven by a
rough path and prove the existence and uniqueness of the solution under an assumption of …

Averaging dynamics driven by fractional Brownian motion

M Hairer, XM Li - 2020 - projecteuclid.org
We consider slow/fast systems where the slow system is driven by fractional Brownian
motion with Hurst parameter H>12. We show that unlike in the case H=12, convergence to …

Some compactness criteria for weak solutions of time fractional PDEs

L Li, JG Liu - SIAM Journal on Mathematical Analysis, 2018 - SIAM
The Aubin--Lions lemma and its variants play crucial roles for the existence of weak
solutions of nonlinear evolutionary PDEs. In this paper, we aim to develop some …

Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains

Z Brzeźniak, Y Li - Transactions of the American Mathematical Society, 2006 - ams.org
We introduce a notion of an asymptotically compact (AC) random dynamical system (RDS).
We prove that for an AC RDS the $\Omega $-limit set $\Omega _B (\omega) $ of any …

Ergodicity of the infinite dimensional fractional Brownian motion

MJ Garrido-Atienza, B Schmalfuß - Journal of Dynamics and Differential …, 2011 - Springer
Ergodicity of the Infinite Dimensional Fractional Brownian Motion Page 1 J Dyn Diff Equat (2011)
23:671–681 DOI 10.1007/s10884-011-9222-5 Ergodicity of the Infinite Dimensional Fractional …

Densities for rough differential equations under Hörmander's condition

T Cass, P Friz - Annals of mathematics, 2010 - JSTOR
We consider stochastic differential equations dY= V (Y) dX driven by a multidimensional
Gaussian process X in the rough path sense [T. Lyons, Rev. Mat. Iberoamericana 14,(1998) …

[HTML][HTML] Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in (1/2, 1)

LH Duc, MJ Garrido-Atienza, A Neuenkirch… - Journal of Differential …, 2018 - Elsevier
This paper addresses the exponential stability of the trivial solution of some types of
evolution equations driven by Hölder continuous functions with Hölder index greater than …

[HTML][HTML] Random dynamical systems, rough paths and rough flows

I Bailleul, S Riedel, M Scheutzow - Journal of Differential Equations, 2017 - Elsevier
We analyze common lifts of stochastic processes to rough paths/rough drivers-valued
processes and give sufficient conditions for the cocycle property to hold for these lifts. We …

Regularity of laws and ergodicity of hypoelliptic SDEs driven by rough paths

M Hairer, NS Pillai - 2013 - projecteuclid.org
We consider differential equations driven by rough paths and study the regularity of the laws
and their long time behavior. In particular, we focus on the case when the driving noise is a …