J. A. D. Appleby, M. Riedle
Published 2007-03-28Version 1
A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic behavior in mean square of a geometric Brownian motion with delay is completely characterized by a sufficient and necessary condition in terms of the drift and diffusion coefficients.
Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations
Weak Solutions of Stochastic Differential Equations over the Field of p-Adic Numbers
Fokker-Planck-Kolmogorov equation for stochastic differential equations with boundary hitting resets
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