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Random Perturbations of Dynamical Systems
M. I. Freĭdlin,A. D. Ventt︠s︡elʹ +1 more
TLDR
In this article, the authors introduce the concept of random perturbations in Dynamical Systems with a Finite Time Interval (FTI) and the Averaging Principle.Abstract:
1.Random Perturbations.- 2.Small Random Perturbations on a Finite Time Interval.- 3.Action Functional.- 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.- 5.Perturbations Leading to Markov Processes.- 6.Markov Perturbations on Large Time Intervals.- 7.The Averaging Principle. Fluctuations in Dynamical Systems with Averaging.- 8.Random Perturbations of Hamiltonian Systems.- 9. The Multidimensional Case.- 10.Stability Under Random Perturbations.- 11.Sharpenings and Generalizations.- References.- Index.read more
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Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
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Evolutionary games on graphs
György Szabó,Gábor Fáth +1 more
TL;DR: The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
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The evolution of conventions
TL;DR: In this article, the authors show how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality, using perturbed Markov processes.
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Learning, mutation, and long run equilibria in games
TL;DR: In this paper, an evolutionary model with a finite number of players and with stochastic mutations is analyzed, and the expansion and contraction of strategies are linked to their current relative success.