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作者：Foss, Sergey; Martin, James B.; Schmidt, Philipp
作者单位：Heriot Watt University; Russian Academy of Sciences; University of Oxford
摘要：We consider directed last-passage percolation on the random graph G = (V, E) where V = Z and each edge (i, j), for i < j is an element of Z, is present in E independently with some probability p is an element of (0, 1]. To every (i, j) is an element of E we attach i.i.d. random weights v(i, j) > 0. We are interested in the behaviour of w(0,n), which is the maximum weight of all directed paths from 0 to n, as n -> infinity. We see two very different types of behaviour, depending on whether E[v(...
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作者：Cox, J. Theodore; Perkins, Edwin A.
作者单位：Syracuse University; University of British Columbia
摘要：We prove a complete convergence theorem for a class of symmetric voter model perturbations with annihilating duals. A special case of interest covered by our results is the stochastic spatial Lotka-Volterra model introduced by Neuhauser and Pacala [Ann. Appl. Probab. 9 (1999) 1226-1259]. We also treat two additional models, the affine and geometric voter models.
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作者：Galichon, A.; Henry-Labordere, P.; Touzi, N.
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
摘要：We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allo...
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作者：Collet, Pierre; Leonardi, Florencia
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute of Physics (INP); Universidade de Sao Paulo
摘要：In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that this bound is in fact realized, namely for almost all realizations of the observed process we can find symbols where the asymptotic exponential rate of loss of memory attains the difference of the first two Lyapunov exponents. These results are derived in par...
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作者：Roberts, Gareth O.; Rosenthal, Jeffrey
作者单位：University of Warwick; University of Toronto
摘要：We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.
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作者：Penda, S. Valere Bitseki; Djellout, Hacene; Guillin, Arnaud
作者单位：Universite Clermont Auvergne (UCA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Institut Universitaire de France
摘要：First, under a geometric ergodicity assumption, we provide some limit theorems and some probability inequalities for the bifurcating Markov chains (BMC). The BMC model was introduced by Guyon to detect cellular aging from cell lineage, and our aim is thus to complete his asymptotic results. The deviation inequalities are then applied to derive first result on the moderate deviation principle (MDP) for a functional of the BMC with a restricted range of speed, but with a function which can be un...
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作者：Pulido, Sergio
作者单位：Carnegie Mellon University
摘要：This paper consists of two parts. In the first part we prove the fundamental theorem of asset pricing under short sales prohibitions in continuoustime financial models where asset prices are driven by nonnegative, locally bounded semimartingales. A key step in this proof is an extension of a wellknown result of Ansel and Stricker. In the second part we study the hedging problem in these models and connect it to a properly defined property of maximality of contingent claims.
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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：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, ...
