4 papers · 1 filter
Lyapunov Exponents for Passive Scalars in White-in-Time Flows
Declan Stacy
We study a passive scalar on the two-dimensional torus driven by an arbitrary finite set of white-in-time divergence-free Fourier modes. We prove that the exponential dissipa…
Asymptotics of Lyapunov Exponents and Phase Transitions for Fluids with Degenerate Forcing
Martin Hairer, Declan Stacy
In this paper we analyze the Lyapunov exponents of a slow-fast system where the slow component is an Ornstein-Uhlenbeck process which perturbs the linear evolution of a fast variab…
Stochastic Persistence in Infinite Dimensions
Juraj Foldes, Declan Stacy
Motivated by infinite-dimensional ecological and biological models such as reaction-diffusion SPDEs and stochastic functional differential equations, we develop a general criteria…
Stochastic Extinction, An Average Lyapunov Function Approach
Juraj Foldes, Declan Stacy
We study the stability of , an invariant subset of a Markov process on a metric space . By building the theory of average Lyapunov fun…