2022

最新文章

• COEXISTENCE FOR A POPULATION MODEL WITH FOREST FIRE EPIDEMICS AI翻译
  作者：Fredes, Luis; Linker, Amitai; Remenik, Daniel
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Universidad Andres Bello; Universidad de Chile; Universidad de Chile
  摘要：We investigate the effect on survival and coexistence of introducing forest fire epidemics to a certain two-species competition model. The model is an extension of the one introduced by Durrett and Remenik (Ann. Appl. Probab. 19 (2009) 1656-1685), who studied a discrete time particle system running on a random 3-regular graph where occupied sites grow until they become sufficiently dense so that an epidemic wipes out large clusters. In our extension we let two species affected by independent e...
• A PROBABILISTIC APPROACH TO CONVEX (φ)-ENTROPY DECAY FOR MARKOV CHAINS AI翻译
  作者：Conforti, Giovanni
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：We study the exponential dissipation of entropic functionals along the semigroup generated by a continuous time Markov chain and the associated convex Sobolev inequalities, including MLSI and Beckner inequalities. We propose a method that combines the Bakry-Emery approach and coupling arguments, which we use as a probabilistic alternative to the discrete Bochner identities. In particular, the validity of the method is not limited to the perturbative setting and we establish convex entropy deca...
• A CLASSIFICATION OF THE DYNAMICS OF THREE-DIMENSIONAL STOCHASTIC ECOLOGICAL SYSTEMS AI翻译
  作者：Hening, Alexandru; Nguyen, Dang H.; Schreiber, Sebastian J.
  作者单位：Tufts University; University of Alabama System; University of Alabama Birmingham; University of California System; University of California Davis
  摘要：The classification of the long-term behavior of dynamical systems is a fundamental problem in mathematics. For both deterministic and stochastic dynamics specific classes of models verify Palis' conjecture: the long-term behavior is determined by a finite number of stationary distributions. In this paper we consider the classification problem for stochastic models of interacting species. For a large class of three-species, stochastic differential equation models, we prove a variant of Palis' c...
• WASSERSTEIN-BASED METHODS FOR CONVERGENCE COMPLEXITY ANALYSIS OF MCMC WITH APPLICATIONS AI翻译
  作者：Qin, Qian; Hobert, James P.
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; State University System of Florida; University of Florida
  摘要：Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. However, results presented herein suggest that d&m may be less useful in the emerging area of convergence complexity analysis, which is the study of how the convergence behavior of Monte Carlo Markov chains scales with sample size, n, and/or number of covariates, p. The problem appears to be that minorization can become a serious liability as dimension in...
• MEAN-FIELD GAMES OF FINITE-FUEL CAPACITY EXPANSION WITH SINGULAR CONTROLS AI翻译
  作者：Campi, Luciano; De Angelis, Tiziano; Ghio, Maddalena; Livieri, Giulia
  作者单位：University of Milan; University of Turin; Collegio Carlo Alberto; Scuola Normale Superiore di Pisa
  摘要：We study Nash equilibria for a sequence of symmetric N-player stochastic games of finite-fuel capacity expansion with singular controls and their mean-field game (MFG) counterpart. We construct a solution of the MFG via a simple iterative scheme that produces an optimal control in terms of a Skorokhod reflection at a (state-dependent) surface that splits the state space into action and inaction regions. We then show that a solution of the MFG of capacity expansion induces approximate Nash equi...
• FAST AND MEMORY-OPTIMAL DIMENSION REDUCTION USING KAC'S WALK AI翻译
  作者：Jain, Vishesh; Pillai, Natesh S.; Sah, Ashwin; Sawhney, Mehtaab; Smith, Aaron
  作者单位：Stanford University; Harvard University; Massachusetts Institute of Technology (MIT); University of Ottawa
  摘要：In this work, we analyze dimension reduction algorithms based on the Kac walk and discrete variants. (1) For n points in R-d, we design an optimal Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be applied to any vector in time O(d log d) for essentially the same restriction on n as in the best-known transforms due to Ailon and Liberty, and Bamberger and Krahmer. Our algorithm is memory-optimal, and outperforms existing algorithms in regimes when n is sufficiently large an...
• FINDING GEODESICS ON GRAPHS USING REINFORCEMENT LEARNING AI翻译
  作者：Kious, Daniel; Mailler, Cecile; Schapira, Bruno
  作者单位：University of Bath; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
  摘要：It is well known in biology that ants are able to find shortest paths between their nest and the food by successive random explorations, without any mean of communication other than the pheromones they leave behind them. This striking phenomenon has been observed experimentally and modelled by different mean-field reinforcement-learning models in the biology literature. In this paper, we introduce the first probabilistic reinforcement-learning model for this phenomenon. In this model, the ants...
• LARGE DEVIATION FOR UNIFORM GRAPHS WITH GIVEN DEGREES AI翻译
  作者：Dhara, Souvik; Sen, Subhabrata
  作者单位：Massachusetts Institute of Technology (MIT); Harvard University
  摘要：Consider the random graph sampled uniformly from the set of all simple graphs with a given degree sequence. Under mild conditions on the degrees, we establish a large deviation principle (LDP) for these random graphs, viewed as elements of the graphon space. As a corollary of our result, we obtain LDPs for functionals continuous with respect to the cut metric, and obtain an asymptotic enumeration formula for graphs with given degrees, subject to an additional constraint on the value of a conti...
• ARE AMERICAN OPTIONS EUROPEAN AFTER ALL? AI翻译
  作者：Christensen, Soeren; Kallsen, Jan; Lenga, Matthias
  作者单位：University of Kiel; Bayer AG
  摘要：We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from (Math. Finance 24 (2014) 156-172; Ann. Inst. H. Poincare Anal. Non Lineaire 18 (2001) 1-17; Ann. Appl. Probab. 12 (2002) 196-223) a...
• MEAN-FIELD MARKOV DECISION PROCESSES WITH COMMON NOISE AND OPEN-LOOP CONTROLS AI翻译
  作者：Motte, Mederic; Huyen Pham
  作者单位：Universite Paris Cite
  摘要：We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such model, called CMKV-MDP for conditional McKean- Vlasov MDP, arises and is obtained here rigorously with a rate of convergence as the asymptotic problem of N-cooperative agents controlled by a social planner/influencer that observes the environment noises but no...