Mean exit time and escape probability for the Ornstein–Uhlenbeck process

2020 ◽  
Vol 30 (9) ◽  
pp. 093127
Author(s):  
Caibin Zeng
Keyword(s):  
Exit Time ◽  
Uhlenbeck Process ◽  
Escape Probability ◽  
Mean Exit Time ◽  
Ornstein Uhlenbeck Process

Mean Exit Time and Escape Probability for Dynamical Systems Driven by Lévy Noises

2014 ◽  
Vol 36 (3) ◽  
pp. A887-A906 ◽  
Author(s):  
T. Gao ◽  
J. Duan ◽  
X. Li ◽  
R. Song
Keyword(s):  
Dynamical Systems ◽  
Exit Time ◽  
Escape Probability ◽  
Mean Exit Time

Parameter estimation via homogenization for stochastic dynamical systems with oscillating coefficients

2018 ◽  
Vol 18 (03) ◽  
pp. 1850025
Author(s):  
Xinyong Zhang ◽  
Hui Wang ◽  
Yanjie Zhang ◽  
Haokun Lin
Keyword(s):  
Parameter Estimation ◽  
Dynamical Systems ◽  
Exit Time ◽  
Least Square Method ◽  
Least Square ◽  
Stochastic Dynamical Systems ◽  
Escape Probability ◽  
Mean Exit Time ◽  
Oscillating Coefficients ◽  
The Mean

This paper is devoted to studying parameter estimation for a class of stochastic dynamical systems with oscillating coefficients. We show that the homogenized systems faithfully capture the dynamical quantities such as mean exit time and escape probability. Exacting data from observations on the mean exit time (or escape probability) of the original systems, we try to fit the mean exit time (or escape probability) of the homogenized systems by least square method. In this way, we can accurately estimate the unknown parameter in the drift under appropriate assumptions. Furthermore, we conduct some numerical experiments to illustrate our method.

scholarly journals MEAN EXIT TIME AND ESCAPE PROBABILITY FOR A TUMOR GROWTH SYSTEM UNDER NON-GAUSSIAN NOISE

2012 ◽  
Vol 22 (04) ◽  
pp. 1250090 ◽  
Author(s):  
JIAN REN ◽  
CHUJIN LI ◽  
TING GAO ◽  
XINGYE KAN ◽  
JINQIAO DUAN
Keyword(s):  
Tumor Growth ◽  
Exit Time ◽  
Laplacian Operator ◽  
Escape Probability ◽  
Tumor Growth Model ◽  
Bifurcation Phenomena ◽  
Mean Exit Time ◽  
Growth System ◽  
The Mean ◽  
Non Gaussian

Effects of non-Gaussian α-stable Lévy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit time and escape probability problems are formulated in a differential-integral equation with a fractional Laplacian operator. Numerical simulations are conducted to evaluate how the mean exit time and escape probability vary or bifurcates when α changes. Some bifurcation phenomena are observed and their impacts are discussed.

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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