Slow Manifolds for Stochastic Koper Models with Stable Lévy Noises

Stochastic dynamics on slow manifolds

The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable simplification. In this article we demonstrate how the same basic methodology may also be applied to stochastic dynamical systems, by examining the behaviour...

Least squares estimators for discretely observed stochastic processes driven by small Lévy noises

AMS 2010 subject classifications: primary 62F12 62M05 secondary 60G52 60J75 Keywords: Asymptotic distribution of LSE Consistency of LSE Discrete observations Least squares method Stochastic processes Parameter estimation Small Lévy noises a b s t r a c t We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impo...

Slow Lévy flights.

Among Markovian processes, the hallmark of Lévy flights is superdiffusion, or faster-than-Brownian dynamics. Here we show that Lévy laws, as well as Gaussian distributions, can also be the limit distributions of processes with long-range memory that exhibit very slow diffusion, logarithmic in time. These processes are path dependent and anomalous motion emerges from frequent relocations to alre...

Extending Stochastic Resonance for Neuron Models to General Lévy Noise

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Lévy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general LEvy noise models. We achieve this by showing that "large jump" discontinuities in the noise can be contr...

Stable Exponentially Harmonic Maps Between Finsler Manifolds