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作者：Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：Lancaster University; University of Toronto
摘要：A phi-irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of Harris recurrence allows us to replace almost all by all, which is potentially important when running Markov chain Monte Carlo algorithms. Full-dimensional Metropolis-Hastings algorithms are known to be Harris recurrent. In this paper, we consider conditions under which Metropolis-within-Gibbs and trans-dimensional M...
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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...
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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 ...
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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 ...
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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...
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作者：Harrison, J. Michael
作者单位：Stanford University
摘要：Due to a printing error the above mentioned article had numerous equations appearing incorrectly in the print version of this paper. The entire article follows as it should have appeared. IMS apologizes to the author and the readers for this error. A recent paper by Harrison and Van Mieghem explained in general mathematical terms how one forms an equivalent workload formulation of a Brownian network model. Denoting by Z(t) the state vector of the original Brownian network, one has a lower dime...
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作者：Mokkadem, Abdelkader; Pelletier, Mariane
作者单位：Universite Paris Saclay
摘要：The first aim of this paper is to establish the weak convergence rate of nonlinear two-time-scale stochastic approximation algorithms. Its second aim is to introduce the averaging principle in the context of two-time-scale stochastic approximation algorithms. We first define the notion of asymptotic efficiency in this framework, then introduce the averaged two-time-scale stochastic approximation algorithm, and finally establish its weak convergence rate. We show, in particular, that both compo...
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作者：Rheinlaender, Thorsten; Steiger, Gallus
作者单位：University of London; London School Economics & Political Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric Levy case or continuous price processes with an orthogonal volatility process. We proceed by linking the entropy measure to a certain semi-linear integro-PDE for which we prove the existence of a classical solution.
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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...
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作者：Wuethrich, Mario V.
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We define a heteropolymer in a medium with random droplets. We prove that for this model we have two regimes: a delocalized one and a localized one. In the localized regime we prove tightness to the droplets, whereas in the delocalized regime we prove diffusive path behavior.
