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math.DS2026
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…
math.DS2026
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…
math.PR2026
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.…