Jump-diffusions with state-dependent switching: existence and uniqueness, Feller property, linearization, and uniform ergodicity

2011 ◽  
Vol 54 (12) ◽  
pp. 2651-2667 ◽  
Author(s):  
FuBao Xi ◽  
Gang Yin
Keyword(s):  
Existence And Uniqueness ◽  
Jump Diffusions ◽  
Feller Property ◽  
State Dependent ◽  
Uniform Ergodicity

scholarly journals Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

2009 ◽  
Vol 46 (1) ◽  
pp. 221-243 ◽  
Author(s):  
Fubao Xi ◽  
G. Yin
Keyword(s):  
Field Model ◽  
Asymptotic Properties ◽  
Mean Field ◽  
Switching Process ◽  
Mean Field Model ◽  
State Dependent ◽  
Uniform Ergodicity ◽  
Continuous State ◽  
Feller Continuity ◽  
Drift Conditions

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

scholarly journals Regularity and stability for the semigroup of jump diffusions with state-dependent intensity

2018 ◽  
Vol 28 (5) ◽  
pp. 3028-3074 ◽  
Author(s):  
Vlad Bally ◽  
Dan Goreac ◽  
Victor Rabiet
Keyword(s):  
Jump Diffusions ◽  
State Dependent

Asymptotic Inference for Jump Diffusions with State-Dependent Intensity

2015 ◽  
Vol 43 (2) ◽  
pp. 520-542 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Bas J.M. Werker
Keyword(s):  
Jump Diffusions ◽  
Asymptotic Inference ◽  
State Dependent

scholarly journals Asymptotic Properties of a Mean-Field Model with a Continuous-State-Dependent Switching Process

2009 ◽  
Vol 46 (01) ◽  
pp. 221-243
Author(s):  
Fubao Xi ◽  
G. Yin
Keyword(s):  
Field Model ◽  
Asymptotic Properties ◽  
Mean Field ◽  
Switching Process ◽  
Mean Field Model ◽  
State Dependent ◽  
Uniform Ergodicity ◽  
Continuous State ◽  
Feller Continuity ◽  
Drift Conditions

This work is concerned with a class of mean-field models given by a switching diffusion with a continuous-state-dependent switching process. Focusing on asymptotic properties, the regularity or nonexplosiveness, Feller continuity, and strong Feller continuity are established by means of introducing certain auxiliary processes and by making use of the truncations. Based on these results, exponential ergodicity is obtained under the Foster–Lyapunov drift conditions. By virtue of the coupling methods, the strong ergodicity or uniform ergodicity in the sense of convergence in the variation norm is established for the mean-field model with a Markovian switching process. Besides this, several examples are presented for demonstration and illustration.

Well Posedness of a Model of Population Dynamics of Infectious Diseases with "Roguing and Replanting" as Strategy of Control

1997 ◽  
Vol 05 (03) ◽  
pp. 403-431 ◽  
Author(s):  
Azeddine Ramzi
Keyword(s):  
Existence And Uniqueness ◽  
Functional Equations ◽  
Integral Functional ◽  
Well Posedness ◽  
Disease Dynamics ◽  
Coupled Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Control Of Epidemics ◽  
Infectious Disease Dynamics

In this paper, we investigate existence and uniqueness of positive solutions of a model of infectious disease dynamics with a strategy for control of epidemics given in [1]. The model presents nonlinear and coupled equations which are transformed to integral functional equations with state dependent delay and solved using a fixed point theorem.

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