On the Asymptotics of an Infinite-Dimensional Stochastic Dynamical System

I am working on an idea where I need to show that, in the long run, a certain infinite-dimensional discrete-time stochastic dynamical system has a stable limiting distribution, and calculate certain properties of that distribution. This notebook is for storing related references. I'm a little paranoid about being scooped, so I won't say much more, only that there are certain connections with genetic algorithms, and that the finite-dimensional analog is related to the replicator equation of evolutionary biology. In that representation, the fitness function would show a particular kind of frequency-dependence, with random fluctuations which are not necessarily independent over time, though I'd be willing to ignore serial dependence if the alternatives were simply intractable. Now, the replicator equation can be re-written as a linear system (or so Nihat tells me), which may be helpful... Update, 4 May 2010: Actually, the project was this paper, and I ended up being able to solve the prob

On the Asymptotics of an Infinite-Dimensional Stochastic Dynamical System Notebooks On the Asymptotics of an Infinite-Dimensional Stochastic Dynamical System Last update : 21 Apr 2025 21:17 First version : 15 June 2006 I am working on an idea where I need to show that, in the long run, a certain infinite-dimensional discrete-time stochastic dynamical system has a stable limiting distribution, and calculate certain properties of that distribution. This notebook is for storing related references. I'm a little paranoid about being scooped, so I won't say much more, only that there are certain con

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