14,909 research outputs found
Comparison theorem of one-dimensional stochastic hybrid delay systems
The comparison theorem of stochastic differential equations has been investigated by many authors. However, little research is available on the comparison theorem of stochastic hybrid systems, which is the topic of this paper. The systems discussed is stochastic delay differential equations with Markovian switching. It is an important class of hybrid systems
On input-to-state stability of stochastic retarded systems with Markovian switching
This note develops a Razumikhin-type theorem on pth moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result
On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations
In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness theorem as well as the almost surely asymptotic behavior for the global solution of highly nonlinear stochastic differential equations with time-varying delay and Markovian switching are discussed by using the Lyapunov function and some stochastic analysis techniques. Two integral lemmas are firstly established to overcome the difficulty stemming from the coexistence of the stochastic perturbation and the time-varying delay. Then, without any redundant restrictive condition on the time-varying delay, by utilizing the integral inequality, the exponential stability in pth(p ≥ 1)-moment for such equations is investigated. By employing the nonnegative semi-martingale convergence theorem, the almost sure exponential stability is analyzed. Finally, two examples are given to show the usefulness of the results obtained.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangxi Province of ChinaFoundation of Jiangxi Provincial Educations of ChinaMinisterio de EconomÃa y Competitividad (MINECO). EspañaJunta de AndalucÃ
Competitive Lotka-Volterra Population Dynamics with Jumps
This paper considers competitive Lotka-Volterra population dynamics with
jumps. The contributions of this paper are as follows. (a) We show stochastic
differential equation (SDE) with jumps associated with the model has a unique
global positive solution; (b) We discuss the uniform boundedness of th
moment with and reveal the sample Lyapunov exponents; (c) Using a
variation-of-constants formula for a class of SDEs with jumps, we provide
explicit solution for 1-dimensional competitive Lotka-Volterra population
dynamics with jumps, and investigate the sample Lyapunov exponent for each
component and the extinction of our -dimensional model.Comment: 25 page
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