[图书][B] Stochastic calculus for fractional Brownian motion and applications
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 …
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 …
rough path and prove the existence and uniqueness of the solution under an assumption of …
Some compactness criteria for weak solutions of time fractional PDEs
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 …
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 …
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 …
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
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) …
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)
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 …
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 …
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
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 …
and their long time behavior. In particular, we focus on the case when the driving noise is a …