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Absorption in stochastic epidemics

Josef Štěpán, Jakub Staněk (2009)

Kybernetika

A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.

Almost sure properties of controlled diffusions and worst case properties of deterministic systems

Martino Bardi, Annalisa Cesaroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.


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