Gaussian unitary ensembles with two jump discontinuities, PDEs, and the coupled Painlevé II and IV systems

2020 ◽  
Vol 146 (1) ◽  
pp. 118-138
Author(s):  
Shulin Lyu ◽  
Yang Chen
Keyword(s):  
Jump Discontinuities ◽  
Painlevé Ii

On Ermakov–Painlevé II systems. Integrable reduction

Meccanica ◽  
2016 ◽  
Vol 51 (12) ◽  
pp. 2967-2974 ◽  
Author(s):  
Colin Rogers ◽  
Wolfgang K. Schief
Keyword(s):  
Painlevé Ii

scholarly journals Bilinear discrete Painleve-II and its particular solutions

1995 ◽  
Vol 28 (12) ◽  
pp. 3541-3548 ◽  
Author(s):  
J Satsuma ◽  
K Kajiwara ◽  
B Grammaticos ◽  
J Hietarinta ◽  
A Ramani
Keyword(s):  
Particular Solutions ◽  
Painlevé Ii

scholarly journals Detecting Strength and Location of Jump Discontinuities in Numerical Data

2013 ◽  
Vol 04 (12) ◽  
pp. 1-14 ◽  
Author(s):  
Philipp Öffner ◽  
Thomas Sonar ◽  
Martina Wirz
Keyword(s):  
Numerical Data ◽  
Jump Discontinuities

scholarly journals TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS

2013 ◽  
Vol 14 (01) ◽  
pp. 1350007 ◽  
Author(s):  
HUIJIE QIAO ◽  
JINQIAO DUAN
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Lévy Processes ◽  
Levy Processes ◽  
Topological Equivalence ◽  
Random Differential Equation ◽  
Jump Discontinuities ◽  
Non Gaussian

After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological equivalence is used to prove the existence of global random attractors.

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