scholarly journals Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process

2006 ◽  
Vol 8 (4) ◽  
pp. 431-447 ◽  
Author(s):  
Julien Chiquet ◽  
Nikolaos Limnios
Keyword(s):  
Dynamical Systems ◽  
Markov Process ◽  
Continuous Time ◽  
Stochastic Dynamical Systems ◽  
Jump Markov Process

scholarly journals Asymptotics of quasi-stationary distributions of small noise stochastic dynamical systems in unbounded domains

2022 ◽  
pp. 1-47
Author(s):  
Amarjit Budhiraja ◽  
Nicolas Fraiman ◽  
Adam Waterbury
Keyword(s):  
Markov Chain ◽  
Dynamical Systems ◽  
Markov Chains ◽  
State Space ◽  
Continuous Time ◽  
Stochastic Dynamical Systems ◽  
Stationary Distributions ◽  
Small Noise ◽  
Positive Orthant ◽  
Limit Points

Abstract We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of the orthant is the absorbing state for the Markov chain and represents the extinction states of different population types. We are interested in the long-term behavior of the Markov chain away from extinction, under a small noise scaling. Under this scaling, the trajectory of the Markov process over any compact interval converges in distribution to the solution of an ordinary differential equation (ODE) evolving in the positive orthant. We study the asymptotic behavior of the quasi-stationary distributions (QSD) in this scaling regime. Our main result shows that, under conditions, the limit points of the QSD are supported on the union of interior attractors of the flow determined by the ODE. We also give lower bounds on expected extinction times which scale exponentially with the system size. Results of this type when the deterministic dynamical system obtained under the scaling limit is given by a discrete-time evolution equation and the dynamics are essentially in a compact space (namely, the one-step map is a bounded function) have been studied by Faure and Schreiber (2014). Our results extend these to a setting of an unbounded state space and continuous-time dynamics. The proofs rely on uniform large deviation results for small noise stochastic dynamical systems and methods from the theory of continuous-time dynamical systems. In general, QSD for Markov chains with absorbing states and unbounded state spaces may not exist. We study one basic family of binomial-Poisson models in the positive orthant where one can use Lyapunov function methods to establish existence of QSD and also to argue the tightness of the QSD of the scaled sequence of Markov chains. The results from the first part are then used to characterize the support of limit points of this sequence of QSD.

scholarly journals Fault Detection and Isolation Scheme in Continuous Time Nonlinear Stochastic Dynamical Systems

2003 ◽  
Vol 36 (5) ◽  
pp. 615-620 ◽  
Author(s):  
A. Castillo ◽  
P.J. Zufiria ◽  
M. Polycarpou ◽  
F. Previdi ◽  
T. Parisini
Keyword(s):  
Dynamical Systems ◽  
Fault Detection ◽  
Continuous Time ◽  
Fault Detection And Isolation ◽  
Stochastic Dynamical Systems

MANAGEMENT OF THE SUCCESS OF STUDENT’S LEARNING BASED ON THE MARKOV MODEL

2018 ◽  
pp. 4-11
Author(s):  
M. V. Noskov ◽  
M. V. Somova ◽  
I. M. Fedotova
Keyword(s):  
Information System ◽  
Markov Process ◽  
Continuous Time ◽  
Information Technologies ◽  
Educational Process ◽  
Automated Information System ◽  
The Subject ◽  
The University ◽  
Independent Work ◽  
Near Future

The article proposes a model for forecasting the success of student’s learning. The model is a Markov process with continuous time, such as the process of “death and reproduction”. As the parameters of the process, the intensities of the processes of obtaining and assimilating information are offered, and the intensity of the process of assimilating information takes into account the attitude of the student to the subject being studied. As a result of applying the model, it is possible for each student to determine the probability of a given formation of ownership of the material being studied in the near future. Thus, in the presence of an automated information system of the university, the implementation of the model is an element of the decision support system by all participants in the educational process. The examples given in the article are the results of an experiment conducted at the Institute of Space and Information Technologies of Siberian Federal University under conditions of blended learning, that is, under conditions when classroom work is accompanied by independent work with electronic resources.

Coherent phenomena in stochastic dynamical systems

1999 ◽  
Vol 169 (2) ◽  
pp. 171 ◽  
Author(s):  
Valerii I. Klyatskin ◽  
D. Gurarie
Keyword(s):  
Dynamical Systems ◽  
Stochastic Dynamical Systems
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