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4 papers
Singular stochastic delay equations driven by fractional Brownian motion: Dynamics, longtime behaviour, and pathwise stability
Mazyar Ghani Varzaneh, Sebastian Riedel
We study differential equations with a linear, path dependent drift and discrete delay in the diffusion term driven by a -Hölder rough path for . We prove well-p…
Invariant Manifolds for Random Parabolic Evolution Equations with almost sectorial operators
M. Ghani Varzaneh, F. Z. Lahbiri, S. Riedel
In this paper, we develop a way of analyzing the random dynamics of stochastic evolution equations with a non-dense domain. Such problems cover several types of evolution equations…
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.