Large deviation principle for dynamical systems coupled with diffusion–transmutation processes

Significance 

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process — where the latter jumps from one mode to another, and thus modifying the dynamics of the system. In particular, we study the exit problem, i.e., an asymptotic estimate for the exit probabilities with which the corresponding processes exit from a given bounded open domain, and then formally prove a large deviation principle for the exit position joint with the type occupation times as the random perturbation vanishes. Moreover, under certain conditions, we also determine the exit place and the type of distribution at the exit time and, as a consequence of this, such information also give the limit of the Dirichlet problem for the corresponding partial differential equation systems with a vanishing small parameter.

Large deviation principle for dynamical systems coupled with diffusion–transmutation processes - Advances in Engineering

About the author

Getachew K. Befekadu received his Ph.D. degree in electrical engineering (with the DAAD scholarship) from the University of Duisburg-Essen, Germany in 2006. He is currently an assistant professor in the Department of Electrical & Computer Engineering, Morgan State University (MSU). Before joining, he was an NRC/AFRL senior research fellow and also affiliated with the Department of Industrial & System Engineering, University of Florida – REEF. He was a research assistant professor/Moreau research fellow at the Department of Electrical Engineering, University of Notre Dame. He was also a postdoctoral research fellow with the Lombardi Comprehensive Cancer Center at Georgetown University, Washington, DC.

His research interests include robust decentralized/distributed control design for large-scale systems, stochastic optimal control problems, asymptotic problems in dynamical systems with small random perturbations, and application of optimization in large-scale systems.

Reference

Befekadu, G. (2019). Large deviation principle for dynamical systems coupled with diffusion–transmutation processes. Systems & Control Letters, 125, 9-15.

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