scholarly journals FIRST EXIT TIMES OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTIPLICATIVE LÉVY NOISE WITH HEAVY TAILS

2011 ◽  
Vol 11 (02n03) ◽  
pp. 495-519 ◽  
Author(s):  
ILYA PAVLYUKEVICH
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Heavy Tails ◽  
Multiplicative Noise ◽  
Exit Time ◽  
Lévy Noise ◽  
Exit Times ◽  
First Exit Time ◽  
First Exit Times ◽  
Levy Noise

In this paper, we study first exit times from a bounded domain of a gradient dynamical system Ẏt = -∇U(Yt) perturbed by a small multiplicative Lévy noise with heavy tails. A special attention is paid to the way the multiplicative noise is introduced. In particular, we determine the asymptotics of the first exit time of solutions of Itô, Stratonovich and Marcus canonical SDEs.

scholarly journals On first exit times and their means for Brownian bridges

2019 ◽  
Vol 56 (3) ◽  
pp. 701-722 ◽  
Author(s):  
Christel Geiss ◽  
Antti Luoto ◽  
Paavo Salminen
Keyword(s):  
Brownian Bridge ◽  
Exit Time ◽  
Three Dimensional ◽  
Exit Times ◽  
First Exit Time ◽  
Binomial Tree ◽  
Brownian Bridges ◽  
Bessel Bridge ◽  
The Mean ◽  
First Exit Times

AbstractFor a Brownian bridge from 0 to y, we prove that the mean of the first exit time from the interval $\left( -h,h \right),h>0$ , behaves as ${\mathrm{O}}(h^2)$ when $h \downarrow 0$ . Similar behaviour is also seen to hold for the three-dimensional Bessel bridge. For the Brownian bridge and three-dimensional Bessel bridge, this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to provide a detailed proof of an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.

scholarly journals Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Lévy noise

2011 ◽  
Vol 16 (0) ◽  
pp. 213-225 ◽  
Author(s):  
Arnaud Debussche ◽  
Michael Hoegele ◽  
Peter Imkeller
Keyword(s):  
Lévy Noise ◽  
Exit Times ◽  
Heavy Tailed ◽  
First Exit Times ◽  
Levy Noise

scholarly journals AN INTERMEDIATE REGIME FOR EXIT PHENOMENA DRIVEN BY NON-GAUSSIAN LÉVY NOISES

2008 ◽  
Vol 08 (03) ◽  
pp. 583-591 ◽  
Author(s):  
ZHIHUI YANG ◽  
JINQIAO DUAN
Keyword(s):  
Dynamical System ◽  
Noise Intensity ◽  
Exit Time ◽  
First Exit Time ◽  
Small Noise ◽  
Intermediate Regime ◽  
Mean Exit Time ◽  
Small Intensity ◽  
The Mean ◽  
Non Gaussian

A dynamical system driven by non-Gaussian Lévy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian Lévy noises, it is shown that the mean exit time is asymptotically faster than exponential (the well-known Gaussian Brownian noise case) but slower than polynomial (the stable Lévy noise case), in terms of the reciprocal of the small noise intensity.

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