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作者：Le Gland, F; Oudjane, N
作者单位：Inria; Electricite de France (EDF)
摘要：We study the stability of the optimal filter w.r.t. its initial condition and w.r.t. the model for the hidden state and the observations in a general hidden Markov model, using the Hilbert projective metric. These stability results are then used to prove, under some mixing assumption, the uniform convergence to the optimal filter of several particle filters, such as the interacting particle filter and some other original particle filters.
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作者：Atar, R; Mandelbaum, A; Reiman, MI
作者单位：Technion Israel Institute of Technology; Technion Israel Institute of Technology; Alcatel-Lucent; Lucent Technologies; AT&T
摘要：We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the numb...
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作者：DeBlassie, RD
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If tau is the first exit time of iterated Brownian motion from the solid, then P(tau > t) can be viewed as a measurement of the amount of contaminant left in the crack at time t. We determine the large time asymptotics of P(tau > t) for both bounded and unbounded sets. We also ...
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作者：Lokka, A; Oksendal, B; Proske, F
作者单位：University of Oslo; Norwegian School of Economics (NHH)
摘要：In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Levy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Levy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d less than or equal to 3, then this solution can be represented as a classical random field in L-2(mu), where mu is th...
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作者：Klüppelberg, C; Kyprianou, AE; Maller, RA
作者单位：Technical University of Munich; Utrecht University; Australian National University; Australian National University
摘要：We formulate the insurance risk process in a general Levy process setting, and give general theorems for the ruin probability and the asymptotic distribution of the overshoot of the process above a high level, when the process drifts to -infinity a.s. and the positive tail of the Levy measure, or of the ladder height measure, is subexponential or, more generally, convolution equivalent. Results of Asmussen and Kluppelberg [Stochastic Process. Appl. 64 (1996) 103-125] and Bertoin and Doney [Adv...
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作者：Silvestrov, DS; Teugels, JL
作者单位：Malardalen University; KU Leuven
摘要：This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems.
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作者：Weissman, T; Merhav, N
作者单位：Stanford University; Technion Israel Institute of Technology
摘要：Let X = {(X-t, Y-t)}(tis an element ofZ) be a stationary time series where X-t is binary valued and Y-t, the noisy observation of X-t, is real valued. Letting P denote the probability measure governing the joint process {(X-t, Y-t)}, we characterize U(l, P), the optimal asymptotic average performance of a predictor allowed to base its prediction for X-t on Y-1,.., Yt-1, where performance is evaluated using the loss function l. It is shown, that the stationarity and ergodicity of P, combined wi...
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作者：Bhattacharya, R; Majumdar, M
作者单位：Indiana University System; Indiana University Bloomington; Cornell University
摘要：Iteration of randomly chosen quadratic maps defines a Markov process: Xn+1 = epsilon(n+1) X-n(1 - X-n), where epsilon(n) are i.i.d. with values in the parameter space [0, 4] of quadratic maps F-theta(x) = thetax(1 - x). Its study is of significance as an important Markov model, with applications to problems of optimization under uncertainty arising in economics. In this article a broad criterion is established for positive Harris recurrence of X-n.
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作者：Bouchard, B; Touzi, N; Zeghal, A
作者单位：Institut Polytechnique de Paris; ENSAE Paris; Sorbonne Universite; Universite PSL; Universite Paris-Dauphine
摘要：We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the shortfall minimization problems in our framework. Second, we allow for the presence of some given liability or a random endowment. In particular, these results provide a dual formulation of the utility ...
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作者：Korolyuk, VS; Limnios, N
作者单位：National Academy of Sciences Ukraine; Institute of Mathematics of NASU; Universite de Technologie de Compiegne
摘要：Stochastic evolutionary systems of additive functional type, described by processes with locally independent increments, are considered with Markov switching in an asymptotic split state space having a stoppage state. The average and diffusion approximation limit theorems are established in both single and double merging. The proofs of these results are obtained using a singular perturbation approach of linear reducible-invertible operators and the tightness of processes. Particular cases of t...
