Author
A. D. Ventt︠s︡elʹ
Bio: A. D. Ventt︠s︡elʹ is an academic researcher. The author has contributed to research in topics: Hamiltonian system & Dynamical systems theory. The author has an hindex of 1, co-authored 1 publications receiving 3873 citations.
Papers
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01 Jan 1984
TL;DR: 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.
4,070 citations
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01 Dec 1992TL;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.
Abstract: Part I. Foundations: 1. Random variables 2. Probability measures 3. Stochastic processes 4. The stochastic integral Part II. Existence and Uniqueness: 5. Linear equations with additive noise 6. Linear equations with multiplicative noise 7. Existence and uniqueness for nonlinear equations 8. Martingale solutions Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations 10. Absolute continuity and Girsanov's theorem 11. Large time behaviour of solutions 12. Small noise asymptotic.
4,042 citations
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.
2,548 citations
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.
Abstract: The author shows how a group of individuals can learn to play a coordination game without any common knowledge and with only a small amount of rationality. The game is repeated many times by different players. Each player chooses an optimal reply based on incomplete information about what other players have done in the past. Occasionally they make mistakes. When the likelihood of mistakes is very small, typically one coordination equilibrium will be played almost all of the time over the long run. This stochastically stable equilibrium can be computed analytically using a general theorem the author proves on perturbed Markov processes. Copyright 1993 by The Econometric Society.
2,444 citations
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2,428 citations
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.
Abstract: An evolutionary model with a finite number of players and with stochastic mutations is analyzed. The expansion and contraction of strategies is linked to their current relative success, but mutuation, perturbing the system from its deterministic evolution, are present as well. The focus is on the long run implications of ongoing mutations, which drastically reduce the set of equilibria. For 2 by 2 symmetric games with two symmetric strict Nash equilibria the risk dominant equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. Copyright 1993 by The Econometric Society.
2,129 citations