-
作者：Mossel, Elchanan; Roch, Sebastien
作者单位：University of California System; University of California Berkeley
摘要：In this paper we study the problem of learning phylogenies and hidden Markov models. We call a Markov model nonsingular if all transition matrices have determinants bounded away from 0 (and 1). We highlight the role OF of the nonsingularity condition for the learning problem. Learning hidden Markov models without the nonsingularity condition is at least as hard as learning parity with noise a well-known learning problem conjectured to be computationally hard. On the other hand, we give a polyn...
-
作者：Denis, Laurent; Martini, Claude
作者单位：Universite Paris Saclay
摘要：The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda. Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. we obtain a partial characterization result and a full characterization which extends Avellaneda...
-
作者：Chow, Pao-Liu
作者单位：Wayne State University
摘要：Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions. the existence theorem fora unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution. in mean-square and the almost sure sense. are studied. Then. ...
-
作者：Devroye, Luc; Hwang, Hsien-Kuei
作者单位：McGill University; Academia Sinica - Taiwan
摘要：We propose a new, direct, correlation-free approach based on central moments of profiles to the asymptotics of width (size of the most abundant level) in some random trees of logarithmic height. The approach is simple but gives precise estimates for expected width, central moments of the width and almost sure convergence. It is widely applicable to random trees of logarithmic height, including recursive trees, binary search trees, quad trees, plane-oriented ordered trees and other varieties of...
-
作者：Neal, Peter; Roberts, Gareth
作者单位：University of Manchester; Lancaster University
摘要：[it this paper we shall consider optimal scaling problems for high-dimensional Metropolis-Hastings algorithms where updates call be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the Metropolis algorithm, Which tunes the overall algorithm acceptance rate to be 0.234. holds for the so-called Metropolis-within-Gibbs algorithm as well. Furthermore. the optimal efficiency obtainable is independent of the dimensionality of the update rule. T...
-
作者：Brockwell, Peter; Chadraa, Erdenebaatar; Lindner, Alexander
作者单位：Colorado State University System; Colorado State University Fort Collins; Technical University of Munich
摘要：A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the COGARCH(1, 1) process of Kluppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601-622], is introduced and studied. The resulting COGARCH(p, q) processes, q >= p >= 1, exhibit many of the characteristic features of observed financial time series, while their corresponding volatility and squared increment processes display a broader range of autocorrelation structures than thos...
-
作者：Hubalek, Friedrich; Kallsen, Jan; Krawczyk, Leszek
作者单位：Aarhus University; Technical University of Munich
摘要：We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as back-ward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formula-,; involve the moment, respectively, cumulant generating function ...
-
作者：Morris, Ben
作者单位：University of California System; University of California Davis
摘要：We obtain a tight bound of O(L(2)logk) for the mixing time of the exclusion process in Z(d)/LZ(d) with k <= (1)/L-2(d) particles. Previously the best bound. based oil the log Sobolev constant determined by Yau was not tight for small k. When dependence on the dimension d is considered. our bounds are all improvement for all k. We also get bounds for the relaxation time that are lower Order in d than previous estimates: our bound of O(L-2 log d) improves oil the earlier bound O(L(2)d) obtained ...
-
作者：Heinrich, Lothar; Schmidt, Hendrik; Schimidt, Volker
作者单位：University of Augsburg; Ulm University
摘要：We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in R-d. This result generalizes all earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640-656] for intersection points of rnotion-invariany Poisson line processes in R-2. Our proof is based oil Hoeffding's decomposition of U-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the method of moments used in...
-
作者：Jonasson, Johan
作者单位：Chalmers University of Technology
摘要：Recently Wilson [Ann, Appl. Probab. 14 (2004) 274-325] introduced an important new technique for lower bounding the mixing time of a Markov chain. In this paper we extend Wilson's technique to find lower bounds of the correct order for card shuffling Markov chains where at each time step a random card is picked and put at the top of the deck. Two classes of such shuffles are addressed, one where the probability that a given card is picked at a given time step depends on its identity, the so-ca...
