scholarly journals Extracting non-Gaussian governing laws from data on mean exit time

2020 ◽  
Vol 30 (11) ◽  
pp. 113112
Author(s):  
Yanxia Zhang ◽  
Jinqiao Duan ◽  
Yanfei Jin ◽  
Yang Li
Keyword(s):  
Exit Time ◽  
Mean Exit Time ◽  
Non Gaussian

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.

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.

A computational analysis for mean exit time under non-Gaussian Lévy noises

2011 ◽  
Vol 218 (5) ◽  
pp. 1845-1856 ◽  
Author(s):  
Huiqin Chen ◽  
Jinqiao Duan ◽  
Xiaofan Li ◽  
Chengjian Zhang
Keyword(s):  
Computational Analysis ◽  
Exit Time ◽  
Mean Exit Time ◽  
Non Gaussian

scholarly journals 1PT004 Mean Exit Time Analysis about Water Molecules around Membrane Surfaces(The 50th Annual Meeting of the Biophysical Society of Japan)

2012 ◽  
Vol 52 (supplement) ◽  
pp. S84
Author(s):  
Eiji Yamamoto ◽  
Takuma Akimoto ◽  
Yoshinori Hirano ◽  
Masato Yasui ◽  
Kenji Yasuoka
Keyword(s):  
Annual Meeting ◽  
Exit Time ◽  
Water Molecules ◽  
Time Analysis ◽  
Membrane Surfaces ◽  
Mean Exit Time ◽  
Biophysical Society

Non-Standard Reduction of Noisy Structural Systems: Shallow Arches

2000 ◽  
Author(s):  
Lalit Vedula ◽  
N. Sri Namachchivaya
Keyword(s):  
Markov Process ◽  
Random Perturbation ◽  
Exit Time ◽  
Stochastic Averaging ◽  
Dimensional System ◽  
Shallow Arches ◽  
Higher Dimensional ◽  
Mean Exit Time ◽  
Stationary Probability Density Function ◽  
Low Dimensional

Abstract The dynamics of a shallow arch subjected to small random external and parametric excitation is invegistated in this work. We develop rigorous methods to replace, in some limiting regime, the original higher dimensional system of equations by a simpler, constructive and rational approximation – a low-dimensional model of the dynamical system. To this end, we study the equations as a random perturbation of a two-dimensional Hamiltonian system. We achieve the model-reduction through stochastic averaging and the reduced Markov process takes its values on a graph with certain glueing conditions at the vertex of the graph. Examination of the reduced Markov process on the graph yields many important results such as mean exit time, stationary probability density function.

Sign in / Sign up

Export Citation Format

Share Document