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Mikko Stenlund: An adiabatic dynamical system as a stochastic process

Abstract: The statistical properties of dynamical systems are traditionally studied in the context of their invariant measures. Motivated by non-equilibrium phenomena in nature, we wish to step out of the above setup. To this end, we introduce a model whose characteristics change slowly with time; hence the word adiabatic in the title. Solving a martingale problem in the spirit of Stroock and Varadhan, we show that repeated observations of the state of the system yield a certain stochastic diffusion process.

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