scholarly journals Propagation of chaos for mean field rough differential equations

2021 ◽  
Vol 49 (2) ◽  
Author(s):  
Ismaël Bailleul ◽  
Rémi Catellier ◽  
François Delarue
Keyword(s):  
Differential Equations ◽  
Mean Field ◽  
Propagation Of Chaos

scholarly journals Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model

2016 ◽  
Vol 166 (2) ◽  
pp. 211-229 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Qitao Yin
Keyword(s):  
Flow Model ◽  
Mean Field ◽  
Propagation Of Chaos ◽  
Pedestrian Flow ◽  
Field Limit ◽  
Mean Field Limit

scholarly journals Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Elena Adomaitienė ◽  
Skaidra Bumelienė ◽  
Gytis Mykolaitis ◽  
Arūnas Tamaševičius
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
Mean Field ◽  
Electrical Circuit ◽  
Voltage Source ◽  
Dc Voltage

A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed.

scholarly journals Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Min ◽  
Ying Peng ◽  
Yongli Qin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Maximum Principles ◽  
Control Problems ◽  
Linear Quadratic Optimal Control ◽  
Fully Coupled

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

Sign in / Sign up

Export Citation Format

Share Document