10 papers
Synchronization by noise for stochastic differential equations driven by fractional Brownian motion
Alexandra Blessing, Mazyar Ghani Varzaneh
We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index . Provided that the SD…
On the negativity of the top Lyapunov exponent for stochastic differential equations driven by fractional Brownian motion
Alexandra Blessing Neamţu, Mazyar Ghani Varzaneh
We provide sign information for the top Lyapunov exponent for a stochastic differential equation driven by fractional Brownian motion. To this aim we analyze the stochastic dynamic…
An integrable bound for semilinear rough partial differential equations with unbounded diffusion coefficients
Alexandra Blessing, Mazyar Ghani Varzaneh
This work develops moment bounds for the controlled rough path norm of the solution of semilinear rough partial differential equations.~The novel aspects are two-fold: first we con…
A mild rough Gronwall Lemma with applications to non-autonomous evolution equations
Alexandra Blessing, Mazyar Ghani Varzaneh, Tim Seitz
We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the C…
Invariant manifolds and stability for rough differential equations
Mazyar Ghani Varzaneh, Sebastian Riedel
We prove the existence of local stable, unstable, and center manifolds for stochastic semiflows induced by rough differential equations driven by rough paths valued stochastic proc…
A general center manifold theorem on fields of Banach spaces
Mazyar Ghani Varzaneh, Sebastian Riedel
A general local center manifold theorem around stationary trajectories is proved for nonlinear cocycles acting on measurable fields of Banach spaces.