Stochastic bifurcation in single-species model induced by α-stable Lévy noise

Nonlinear stochastic equations with multiplicative Lévy noise.

The Langevin equation with a multiplicative Lévy white noise is solved. The noise amplitude and the drift coefficient have a power-law form. A validity of ordinary rules of the calculus for the Stratonovich interpretation is discussed. The solution has the algebraic asymptotic form and the variance may assume a finite value for the case of the Stratonovich interpretation. The problem of escapin...

Stochastic Resonance in Chua’s Circuit Driven by Alpha-stable Noise

Emergent Lévy behavior in single-cell stochastic gene expression.

Single-cell gene expression is inherently stochastic; its emergent behavior can be defined in terms of the chemical master equation describing the evolution of the mRNA and protein copy numbers as the latter tends to infinity. We establish two types of "macroscopic limits": the Kurtz limit is consistent with the classical chemical kinetics, while the Lévy limit provides a theoretical foundation...

Stochastic Euler equations of fluid dynamics with Lévy noise

In this work we prove the existence and uniqueness of pathwise solutions up to a stopping time to the stochastic Euler equations perturbed by additive and multiplicative Lévy noise in two and three dimensions. The existence of a unique maximal solution is also proved.

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...