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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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answer
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When is a stationary measure of a Markov chain "exponentially localized"?
Here exponentially localized can be thought in a non-rigorous manner as a measure that is mostly supported on a sparse number of nodes.
Some intuition can gained by thinking about a diffusion process, …
3
votes
Accepted
PDE-oriented textbook on probability and random processes?
Stochastic processes and application by Pavliotis is a good one.
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Singular distributions: Applications and Instances
The notion of Smale horseshoe in dynamical systems involves construction of cantor sets. Smale horseshoe is a central concept in modern dynamical systems theory, and as such, provides a model for vari …
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Finding cohesive (low exit probability) sets in a Markov process
In probabilistic approach to dynamical systems and related literature, what you call 'cohesive' sets are known as almost-invariant sets, coherent sets or meta-stable sets. Here, we are usually interes …