5 papers
Persistence in probability for stochastic delay equations with multiplicative noise
Mark van den Bosch, John Ioannis Stavroulakis
We study the stochastic delay equation \begin{equation*} dX(t)=[-γX(t)+r f(X(t-τ))]\,dt+σX(t)\,dW(t), \end{equation*} where , , and with eit…
Stochastic Mackey-Glass Equations and Other Negative Feedback Systems: Existence of Invariant Measures
Mark van den Bosch, Onno van Gaans, Sjoerd Verduyn Lunel
We study equations like the Mackey-Glass equations and Nicholson's blowflies equation, each perturbed by a (small) multiplicative noise term. Solutions to these stochastic negative…
Stochastic Wright's Equation: Existence of Invariant Measures
Mark van den Bosch, Onno van Gaans, Sjoerd Verduyn Lunel
Wright's delay differential equation is one of the prime examples of a fully nonlinear equation without an explicit solution and whose dynamics can be understood by analytic means.…
Existence of Invariant Probability Measures for Stochastic Differential Equations with Finite Time Delay
Mark van den Bosch, Onno van Gaans, Sjoerd Verduyn Lunel
We provide sufficient conditions for the existence of invariant probability measures for generic stochastic differential equations with finite time delay. This is achieved by means…
Multidimensional Stability of Planar Travelling Waves for Stochastically Perturbed Reaction-Diffusion Systems
Mark van den Bosch, Hermen Jan Hupkes
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invarian…