3 citations · 5 across the 11 of their papers we have counts for
13 papers
Invariant Manifolds and Stability for Singular SPDEs
Mazyar Ghani Varzaneh
We study the long-time dynamics of a class of singular stochastic partial differential equations with multiplicative Gaussian noise. Using the theory of regularity structures, we c…
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.
An integrable bound for rough stochastic partial differential equations with applications to invariant manifolds and stability
Mazyar Ghani Varzaneh, Sebastian Riedel
We study semilinear rough stochastic partial differential equations as introduced in [Gerasimovi{č}s, Hairer; EJP 2019]. We provide -integrable a priori bounds fo…
Introduction to rough paths theory
Mazyar Ghani Varzaneh, Sebastian Riedel
These notes are an extended version of the course "Introduction to rough paths theory" given at the XXV Brazilian School of Probability in Campinas in August 2022. Their aim is to…
The geometry of controlled rough paths
Mazyar Ghani Varzaneh, Sebastian Riedel, Alexander Schmeding +1
We prove that the spaces of controlled (branched) rough paths of arbitrary order form a continuous field of Banach spaces. This structure has many similarities to an (infinite-dime…
A dynamical theory for singular stochastic delay differential equations II: Nonlinear equations and invariant manifolds
Mazyar Ghani Varzaneh, Sebastian Riedel
Building on results obtained in [GVRS], we prove Local Stable and Unstable Manifold Theorems for nonlinear, singular stochastic delay differential equations. The main tools are rou…
Oseledets splitting and invariant manifolds on fields of Banach spaces
Mazyar Ghani Varzaneh, Sebastian Riedel
We prove a semi-invertible Oseledets theorem for cocycles acting on measurable fields of Banach spaces, i.e. we only assume invertibility of the base, not of the operator. As an ap…
A dynamical theory for singular stochastic delay differential equations I: Linear equations and a Multiplicative Ergodic Theorem on fields of Banach spaces
Mazyar Ghani Varzaneh, Sebastian Riedel, Michael Scheutzow
We show that singular stochastic delay differential equations (SDDEs) induce cocycle maps on a field of Banach spaces. A general Multiplicative Ergodic Theorem on fields of Banach…