# Dynamics and absorption properties of stochastic equations with Hölder diffusion coefficients

@article{Touboul2012DynamicsAA, title={Dynamics and absorption properties of stochastic equations with H{\"o}lder diffusion coefficients}, author={Jonathan Touboul and Gilles Wainrib}, journal={Physica D: Nonlinear Phenomena}, year={2012}, volume={307}, pages={42-60} }

## 8 Citations

Long-term behaviour of asymptotically autonomous Hamiltonian systems with multiplicative noise

- Mathematics
- 2022

. The inﬂuence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the…

Bifurcations in asymptotically autonomous Hamiltonian systems under multiplicative noise

- Mathematics
- 2021

Abstract. The effect of multiplicative stochastic perturbations on Hamiltonian systems on the plane is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium…

A Mathematical Framework for Critical Transitions: Normal Forms, Variance and Applications

- MathematicsJ. Nonlinear Sci.
- 2013

It is shown that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit andStochastic fluctuations are analyzed and scaling laws of the variance of stochastic sample paths near critical transitions for fast-subsystem bifURcations up to codimension two are calculated.

Two paradigmatic scenarios for inverse stochastic resonance.

- PhysicsChaos
- 2020

Two generic scenarios for inverse stochastic resonance are demonstrated by considering a paradigmatic model of two adaptively coupled stochastically active rotators whose local dynamics is close to a bifurcation threshold by explaining the mechanisms behind the resonant effect in terms of slow-fast analysis of the corresponding noiseless systems.

Central limit theorems of range-based estimators for diffusion models

- MathematicsCommunications in Statistics - Theory and Methods
- 2019

Abstract In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify…

Synchronized stationary distribution and synchronization for memristor-based complex networks via intermittent control

- MathematicsApplicable Analysis
- 2020

Synchronized stationary distribution and exponential synchronization analysis for stochastic memristor-based complex networks are investigated and it is pointed out that aperiodically intermittently intermittent synchronization errors are observed.

Optimal harvesting for a logistic growth model with predation and a constant elasticity of variance

- MathematicsAnn. Oper. Res.
- 2018

An appropriate version of the dynamic programming principle is developed for the problem of optimal management of renewable resources such as agricultural commodities and fishery production, to provide a characterization of the optimal harvesting strategies and discuss some qualitative properties of the corresponding value function.

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