Universiteit Leiden

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Long term dynamics of stochastic evolution equations

Promotor: S.M. Verduyn Lunel, Co-promotor: O. van Gaans

Joris Bierkens
09 februari 2010
Thesis in Leiden Repository

Stochastic differential equations with delay are the inspiration for this thesis. Examples of such equations arise in population models, control systems with delay and noise, lasers, economical models, neural networks, environmental pollution and in many other situations. In such models we are often interested in the evolution of a particular quantity, for example the size of a population, or the amount of pollution in a particular area, changing in time. A differential equation with delay, or delay equation, is a differential equation in which the change in time of such a quantity is expressed as a function of the value of that quantity at different points in time, in the past as well as in the present. This is in contrast with an ordinary differential equation, in which the change in time of the quantity at a specific time is expressed as a function of that quantity at that specific time only.

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