4期

最新文章

• APPROXIMATION OF STOCHASTIC PROCESSES BY NONEXPANSIVE FLOWS AND COMING DOWN FROM INFINITY AI翻译
  作者：Bansaye, Vincent
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
  摘要：This paper deals with the approximation of semimartingales in finite dimension by dynamical systems. We give trajectorial estimates uniform with respect to the initial condition for a well-chosen distance. This relies on a nonexpansivity property of the flow and allows to consider non-Lipschitz vector fields. The fluctuations of the process are controlled using the martingale technics and stochastic calculus. Our main motivation is the trajectorial description of stochastic processes starting ...
• LARGE DEVIATIONS FOR FAST TRANSPORT STOCHASTIC RDES WITH APPLICATIONS TO THE EXIT PROBLEM AI翻译
  作者：Cerrai, Sandra; Paskal, Nicholas
  作者单位：University System of Maryland; University of Maryland College Park
  摘要：We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the regime where the relative sizes of the diffusion and reaction terms are different. Specifically, we consider the case where the diffusion rate is much larger than the rate of reaction, and the deterministic rate of reaction is much larger than either of the r...
• ON SKOROKHOD EMBEDDINGS AND POISSON EQUATIONS AI翻译
  作者：Doering, Leif; Gonon, Lukas; Proemel, David J.; Reichmann, Oleg
  作者单位：University of Mannheim; University of Oxford
  摘要：The classical Skorokhod embedding problem for a Brownian motion W asks to find a stopping time tau so that W-tau is distributed according to a prescribed probability distribution mu. Many solutions have been proposed during the past 50 years and applications in different fields emerged. This article deals with a generalized Skorokhod embedding problem (SEP): Let X be a Markov process with initial marginal distribution mu(0) and let mu(1) be a probability measure. The task is to find a stopping...
• MIXING TIME ESTIMATION IN REVERSIBLE MARKOV CHAINS FROM A SINGLE SAMPLE PATH AI翻译
  作者：Hsu, Daniel; Kontorovich, Aryeh; Levin, David A.; Peres, Yuval; Szepesvari, Csaba; Wolfer, Geoffrey
  作者单位：Columbia University; Columbia University; Ben-Gurion University of the Negev; University of Oregon; Microsoft; University of Alberta
  摘要：The spectral gap gamma(star) of a finite, ergodic and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix P may be unknown, yet one sample of the chain up to a fixed time n may be observed. We consider here the problem of estimating gamma(star) from this data pi Let p be the stationary distribution of P, and pi(star) = min(x) pi(x). We show that if n is at least 1/gamma(star)pi(star) times a logarithmic correcti...
• A PROBABILISTIC APPROACH TO DIRAC CONCENTRATION IN NONLOCAL MODELS OF ADAPTATION WITH SEVERAL RESOURCES AI翻译
  作者：Champagnat, Nicolas; Henry, Benoit
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; IMT - Institut Mines-Telecom; Universite de Lille; IMT Nord Europe
  摘要：This work is devoted to the study of scaling limits in small mutations and large time of the solutions u(epsilon) of two deterministic models of phenotypic adaptation, where the parameter epsilon > 0 scales the size or frequency of mutations. The second model is the so-called Lotka-Volterra parabolic PDE in Rd with an arbitrary number of resources and the first one is a version of the second model with finite phenotype space. The solutions of such systems typically concentrate as Dirac masses ...
• PROPAGATION OF CHAOS FOR TOPOLOGICAL INTERACTIONS AI翻译
  作者：Degond, P.; Pulvirenti, M.
  作者单位：Imperial College London; University of L'Aquila
  摘要：We consider a N-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit N -> infinity, as following from the previous analysis in (J. Stat. Phys. 163 (2016) 41-60) can be rigorously derived. This means that the statistical independence (propagation of chaos) is indeed recovered in the limit, provided it is assumed at time zero.
• CRITICAL POINT FOR INFINITE CYCLES IN A RANDOM LOOP MODEL ON TREES AI翻译
  作者：Hammond, Alan; Hegde, Milind
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：We study a spatial model of random permutations on trees with a time parameter T > 0, a special case of which is the random stirring process. The model on trees was first analysed by Bjornberg and Ueltschi [Ann. Appl. Probab. 28 (2018) 2063-2082], who established the existence of infinite cycles for T slightly above a putatively identified critical value but left open behaviour at arbitrarily high values of T. We show the existence of infinite cycles for all T greater than a constant, thus cla...
• ITERATIVE MULTILEVEL PARTICLE APPROXIMATION FOR MCKEAN-VLASOV SDES AI翻译
  作者：Szpruch, Lukasz; Tan, Shuren; Tse, Alvin
  作者单位：University of Edinburgh
  摘要：The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean (Proc. Natl. Acad. Sci. USA 56 (1966) 1907-1911) as they pave a way to probabilistic representations for many important nonlinear/nonlocal PDEs. The fact that particles are not independent render classical variance reduction techniques not directly applicable, and consequently make simulations of interacting diffusions prohibitive. I...