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Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics

M. Aguiar, B.W. Kooi, J. Martins, N. Stollenwerk (2012)

Mathematical Modelling of Natural Phenomena

In this paper we analyze the stochastic version of a minimalistic multi-strain model, which captures essential differences between primary and secondary infections in dengue fever epidemiology, and investigate the interplay between stochasticity, seasonality and import. The introduction of stochasticity is needed to explain the fluctuations observed in some of the available data sets, revealing a scenario where noise and complex deterministic skeleton...

Set-valued random differential equations in Banach space

Mariusz Michta (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider the problem of the existence of solutions of the random set-valued equation: (I) D H X t = F ( t , X t ) P . 1 , t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space K c ( E ) , of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.

Set-valued stochastic integrals and stochastic inclusions in a plane

Władysław Sosulski (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We present the concepts of set-valued stochastic integrals in a plane and prove the existence of a solution to stochastic integral inclusions of the form z s , t φ s , t + 0 s 0 t F u , v ( z u , v ) d u d v + 0 s 0 t G u , v ( z u , v ) d w u , v

Stochastic flow for SDEs with jumps and irregular drift term

Enrico Priola (2015)

Banach Center Publications

We consider non-degenerate SDEs with a β-Hölder continuous and bounded drift term and driven by a Lévy noise L which is of α-stable type. If β > 1 - α/2 and α ∈ [1,2), we show pathwise uniqueness and existence of a stochastic flow. We follow the approach of [Priola, Osaka J. Math. 2012] improving the assumptions on the noise L. In our previous paper L was assumed to be non-degenerate, α-stable and symmetric. Here we can also recover relativistic and truncated stable processes and some classes...

Superposition rules and stochastic Lie–Scheffers systems

Joan-Andreu Lázaro-Camí, Juan-Pablo Ortega (2009)

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

This paper proves a version for stochastic differential equations of the Lie–Scheffers theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution properties of the distribution generated by the vector fields that define it. When stated in the particular case of standard deterministic systems, our main theorem improves various aspects of the classical Lie–Scheffers result. We show that the stochastic analog...

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.

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