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作者：Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F.
作者单位：Ruprecht Karls University Heidelberg; University of Bern
摘要：This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Ito semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.
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作者：Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or non-Markovian) case for a general stochastic control problem. A general convergence result is obtained by a weak convergence method in the spirit of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time (1992) Springer]. We also get a r...
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作者：Ouchard, Bruno B.; Moreau, Ludovic; Nutz, Marcel
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris; Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
摘要：We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed geometric dynamic programming principle for this problem and derive, for the case of a controlled SDE, the corresponding dynamic programming equation in the sense of viscosity solutions. As an example, we consider a problem of partial hedging under Knightian unce...
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作者：Alexander, Kenneth S.; Zygouras, Nikos
作者单位：University of Southern California; University of Warwick
摘要：We study the path properties of a random polymer attracted to a defect line by a potential with disorder, and we prove that in the delocalized regime, at any temperature, the number of contacts with the defect line remains in a certain sense tight in probability as the polymer length varies. On the other hand we show that at sufficiently low temperature, there exists a.s. a subsequence where the number of contacts grows like the log of the length of the polymer.
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作者：Smith, Aaron
作者单位：Brown University
摘要：We determine the mixing time of a simple Gibbs sampler on the unit simplex, confirming a conjecture of Aldous. The upper bound is based on a two-step coupling, where the first step is a simple contraction argument and the second step is a non-Markovian coupling. We also present a MCMC-based perfect sampling algorithm based on our proof which can be applied with Gibbs samplers that are harder to analyze.
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作者：Kang, Hye-Won; Kurtz, Thomas G.; Popovic, Lea
作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Concordia University - Canada
摘要：Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit the...
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作者：Maillard, Pascal; Zeitouni, Ofer
作者单位：Weizmann Institute of Science
摘要：Consider a d-ary rooted tree (d >= 3) where each edge e is assigned an i.i.d. (bounded) random variable X (e) of negative mean. Assign to each vertex v the sum S(v) of X (e) over all edges connecting v to the root, and assume that the maximurn S-n* of S(v) over all vertices v at distance n from the root tends to infinity (necessarily, linearly) as n tends to infinity. We analyze the Metropolis algorithm on the tree and show that under these assumptions there always exists a temperature 1/beta ...
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作者：Chassagneux, Jean-Francois; Crisan, Dan
作者单位：Imperial College London
摘要：We study the convergence of a class of Runge-Kutta type schemes for backward stochastic differential equations (BSDEs) in a Markovian framework. The schemes belonging to the class under consideration benefit from a certain stability property. As a consequence, the overall rate of the convergence of these schemes is controlled by their local truncation error. The schemes are categorized by the number of intermediate stages implemented between consecutive partition time instances. We show that t...
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作者：Eberle, Andreas
作者单位：University of Bonn
摘要：The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the MALA chain with semi-implicit Euler proposals applied to log-concave probability measures that have a density w.r.t. a Gaussian reference measure. For sufficiently regular densities, the estimates are dimension-independent, and they hold for sufficiently sma...
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作者：Ettinger, Boris; Evans, Steven N.; Hening, Alexandru
作者单位：Princeton University; University of California System; University of California Berkeley; University of Oxford
摘要：The inverse first passage time problem asks whether, for a Brownian motion B and a nonnegative random variable zeta, there exists a time-varying barrier b such that P{B-s > b(s), O <= s <= t} > P{zeta < t}. We study a smoothed version of this problem and ask whether there is a barrier b such that E[exp(-lambda integral(t)(O) psi (B-s - b(s)) ds)] = P{zeta > t}, where lambda is a killing rate parameter, and psi : R -> [0, 1] is a nonincreasing function. We prove that if psi is suitably smooth, ...
