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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 ...
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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...
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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...
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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...
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作者：Fukushima, Ryoki; Junk, Stefan
作者单位：Kyoto University; Technical University of Munich
摘要：We study a continuum model of directed polymer in random environment. The law of the polymer is defined as the Brownian motion conditioned to survive among space-time Poissonian disasters. This model is well studied in the positive temperature regime. However, at zero-temperature, even the existence of the free energy has not been proved. In this article, we show that the free energy exists and is continuous at zero-temperature.
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作者：Leobacher, Gunther; Szoelgyenyi, Michaela
作者单位：University of Graz; University of Klagenfurt
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作者：Van Hao Can
作者单位：Vietnam Academy of Science & Technology (VAST)
摘要：In a recent paper, Giardina et al. [ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016) 121-161] have proved a law of large number and a central limit theorem with respect to the annealed measure for the magnetization of the Ising model on some random graphs, including the random 2-regular graph. In this paper, we present a new proof of their results which applies to all random regular graphs. In addition, we prove the existence of annealed pressure in the case of configuration model random graphs.
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作者：De, Anindya; O'Donnell, Ryan; Servedio, Rocco A.
作者单位：Northwestern University; Carnegie Mellon University; Columbia University
摘要：In the (deletion-channel) trace reconstruction problem, there is an unknown n-bit source string x. An algorithm is given access to independent traces of x, where a trace is formed by deleting each bit of x independently with probability delta. The goal of the algorithm is to recover x exactly (with high probability), while minimizing samples (number of traces) and running time. Previously, the best known algorithm for the trace reconstruction problem was due to Holenstein et al. [in Proceeding...
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作者：Yilmaz, Atilla; Zeitouni, Ofer
作者单位：Koc University; New York University; Weizmann Institute of Science
摘要：We consider a finite horizon stochastic optimal control problem for nearest-neighbor random walk {X-i} on the set of integers. The cost function is the expectation of the exponential of the path sum of a random stationary and ergodic bounded potential plus theta X-n. The random walk policies are measurable with respect to the random potential, and are adapted, with their drifts uniformly bounded in magnitude by a parameter delta is an element of [0, 1]. Under natural conditions on the potentia...
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作者：Junnila, Janne; Saksman, Eero; Webb, Christian
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Norwegian University of Science & Technology (NTNU); University of Helsinki; Aalto University
摘要：In this article, we establish novel decompositions of Gaussian fields taking values in suitable spaces of generalized functions, and then use these decompositions to prove results about Gaussian multiplicative chaos. We prove two decomposition theorems. The first one is a global one and says that if the difference between the covariance kernels of two Gaussian fields, taking values in some Sobolev space, has suitable Sobolev regularity, then these fields differ by a Holder continuous Gaussian ...
