# Scaling limit for the diffusion exit problem in the Levinson case

@article{Monter2010ScalingLF, title={Scaling limit for the diffusion exit problem in the Levinson case}, author={Sergio A. Almada Monter and Yuri Bakhtin}, journal={Stochastic Processes and their Applications}, year={2010}, volume={121}, pages={24-37} }

## 10 Citations

### Scaling limits and exit law for multiscale diffusions

- MathematicsAsymptot. Anal.
- 2014

The first order Langevin equation is applied to the exit problem for multiscale diffusions, deriving the limiting law of the joint distribution of the exit time and exit location.

### Scaling limit for the diffusion exit problem

- Mathematics, Computer Science
- 2011

This dissertation proves a scaling limit for the exit of a domain problem of a small noise system with underlying hyperbolic dynamics and proposes a pathwise approach based on the theory of normal forms combined with geometrical arguments to provide the state of the art results in related problems.

### Scaling limits for conditional diffusion exit problems and asymptotics for nonlinear elliptic equations

- Mathematics
- 2015

The goal of this paper is to supplement the large deviation principle of the Freidlin–Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind.…

### Scaling Limit for the Diffusion Exit Problem, a Survey

- Mathematics
- 2014

In this review, an outline of the so called Freidlin-Wentzell theory and its recent extensions is given. Broadly, this theory studies the exponential rate at which the probabilities of rare events…

### Scaling limits for conditional diffusion exit problems, Doob's h-transform, and asymptotics for nonlinear elliptic equations

- Mathematics
- 2013

The goal of this paper is to supplement the large deviation principle of the Freidlin--Wentzell theory on exit problems for diffusion processes with results of classical central limit theorem kind.…

### On Gumbel limit for the length of reactive paths

- Mathematics
- 2013

We give a new proof of the vanishing noise limit theorem for exit times of one-dimensional diffusions conditioned on exiting through a point separated from the starting point by a potential wall. We…

### Universal Statistics of Incubation Periods and Other Detection Times via Diffusion Models

- Computer ScienceBulletin of mathematical biology
- 2019

The character of the models allows us to argue that the features of the exit time distributions that are described are universal and manifest themselves in various other situations where the times involved can be described as detection or halting times, for example response times studied in psychology.

### Hitting time of rapid intensification onset in hurricane-like vortices

- Environmental Science, PhysicsPhysics of Fluids
- 2021

Predicting tropical cyclone (TC) rapid intensification (RI) is an important yet challenging task in current operational forecast due to our incomplete understanding of TC nonlinear processes. This…

### Scaling limit for escapes from unstable equilibria in the vanishing noise limit: Nontrivial Jordan block case

- Mathematics, PhysicsStochastics and Dynamics
- 2019

We consider white noise perturbations of a nonlinear dynamical system in the neighborhood of an unstable critical point with linearization given by a Jordan block of full dimension. For the…

### Normal forms approach to diffusion near hyperbolic equilibria

- Mathematics
- 2010

We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighbourhood of a hyperbolic critical point. We show that if the distribution of the…

## References

SHOWING 1-9 OF 9 REFERENCES

### Small noise limit for diffusions near heteroclinic networks

- Mathematics
- 2010

This is a nontechnical exposition of the theory on vanishing noise limit for random perturbations of dynamical systems admitting heteroclinic networks developed by the author [Y. Bakhtin, Noisy…

### Markov Processes and Di+erential Equations: Asymptotic Problems

- Mathematics
- 1996

1 Stochastic Processes Defined by ODE's.- 2 Small Parameter in Higher Derivatives: Levinson's Case.- 3 The Large Deviation Case.- 4 Averaging Principle for Stochastic Processes and for Partial…

### Random Perturbations of Dynamical Systems

- Mathematics, Physics
- 1984

1.Random Perturbations.- 2.Small Random Perturbations on a Finite Time Interval.- 3.Action Functional.- 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.-…

### Noisy heteroclinic networks

- Environmental Science
- 2003

The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching…

### Diffusion Processes Depending on a Small Parameter

- Mathematics
- 1962

In this paper we consider a random disturbance of a system of ordinary differential equations which can be written in vector form as follows: \[ x( t ) = a ( {t,x} ), x( 0 ) = x_0 ,\quad t \in […

### Brownian Motion and Stochastic Calculus

- Mathematics
- 2008

1 Preliminaries of Measure Theory De
nition 1 F P ( ) is said to be an algebra if (1) 2 F (2) A;B 2 F implies A S B 2 F (3) A 2 F implies AC 2 F . F is said to be a semialgebra or semi-ring is (1) ;?…

### Graduate Texts in Mathematics

- Education
- 1982

Graduate Texts in Mathematics bridge the gap between passive study and creative understanding, offering graduate-level introductions to advanced topics in mathematics. The volumes are carefully…