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Synchronization of time-delayed systems with discontinuous coupling

Hong-jun Shi, Lian-ying Miao, Yong-zheng Sun (2017)

Kybernetika

This paper concerns the synchronization of time-delayed systems with periodic on-off coupling. Based on the stability theory and the comparison theorem of time-delayed differential equations, sufficient conditions for complete synchronization of systems with constant delay and time-varying delay are established. Compared with the results based on the Krasovskii-Lyapunov method, the sufficient conditions established in this paper are less restrictive. The theoretical results show that two time-delayed...

Systems of differential equations modeling non-Markov processes

Irada Dzhalladova, Miroslava Růžičková (2023)

Archivum Mathematicum

The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.

Variational representations for continuous time processes

Amarjit Budhiraja, Paul Dupuis, Vasileios Maroulas (2011)

Annales de l'I.H.P. Probabilités et statistiques

A variational formula for positive functionals of a Poisson random measure and brownian motion is proved. The formula is based on the relative entropy representation for exponential integrals, and can be used to prove large deviation type estimates. A general large deviation result is proved, and illustrated with an example.

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