Journal ArticleDOI
On the theory of brownian motion
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The spectrum of the Fokker-Planck operator for weakly coupled gases is considered in this paper, where the operator is decomposed into operators acting on functions whose angular dependence is given by spherical harmonics.Abstract:
The spectrum of the Fokker-Planck operator for weakly coupled gases is considered. The operator is decomposed into operators acting on functions whose angular dependence is given by spherical harmonics. It is shown that the operator corresponding to l = 0 has zero for a point eigenvalue (the eigenfunction is the Maxwell distribution). There are no other point eigenvalues and the continuous spectrum of all of the operators is the entire negative real axis. Some consequences are briefly discussed.read more
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Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
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Foundations of modern probability
TL;DR: In this article, the authors discuss the relationship between Markov Processes and Ergodic properties of Markov processes and their relation with PDEs and potential theory. But their main focus is on the convergence of random processes, measures, and sets.
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Lévy Processes and Stochastic Calculus
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
Journal ArticleDOI
Natural selection and random genetic drift in phenotypic evolution.
TL;DR: The concept of adaptive zones is clarified by the construction of an adaptive topography for the average phenotype in a population, which shows that with constant fitnesses theaverage phenotype evolves toward the nearest adaptive zone in the phenotype space, but if fitnesses are frequency-dependent the average phenotypes may evolve away from an adaptive zone.
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Stochastic climate models Part I. Theory
TL;DR: In this article, a stochastic model of climate variability is considered in which slow changes of climate are explained as the integral response to continuous random excitation by short period "weather" disturbances.
References
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Book
Non-equilibrium statistical mechanics
Ilya Prigogine,R. Landshoff +1 more
TL;DR: In this article, the Liouville equation is used to relate the memory function to the time correlation function of the fluctuations of the fluxes, a key result in modern non-equilibrium statistical mechanics.
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