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作者：Ivanoff, BG; Merzbach, E
作者单位：University of Ottawa; Bar Ilan University
摘要：Using the theory of set-indexed martingales, we develop a general model for survival analysis with censored data which is parameterized by sets instead of time points. We define a set-indexed Nelson-Aalen estimator for the integrated hazard function with the presence of a censoring by a random set which is a stopping set. We prove that this estimator is asymptotically unbiased and consistent. A central limit theorem is given. This model can be applied to cases when censoring occurs in geometri...
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作者：Jourdain, B
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：in this paper, we are interested in approximating the entropy solution of a one-dimensional inviscid scalar conservation law, starting from an initial condition with bounded variation owing to a system of interacting diffusions. We modify the system of signed particles associated with the parabolic equation obtained from the addition of a viscous term to this equation by killing couples of particles with opposite sign that merge. The sample paths of the corresponding reordered particles can be...
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作者：Ma, J; Protter, P; San Martín, J; Torres, S
作者单位：Purdue University System; Purdue University; Cornell University; Universidad de Chile; Universidad de Valparaiso
摘要：We propose a method for numerical approximation of backward stochastic differential equations. Our method allows the final condition of the equation to be quite general and simple to implement. It relies on an approximation of Brownian motion by simple random walk.
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作者：Paulsen, J
作者单位：University of Bergen
摘要：We consider a classical risk process compounded by another independent process. Both of these component processes are assumed to be Levy processes. We show asymptotically that as initial capital y increases the ruin probability will essentially behave as y(-k), where K depends on one of the component processes.
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作者：Basrak, B; Davis, RA; Mikosch, T
作者单位：Colorado State University System; Colorado State University Fort Collins; University of Copenhagen
摘要：We establish the equivalence between the multivariate regular variation of a random vector and the univariate regular variation of all linear combinations of the components of such a vector. According to a classical result of Kesten [Acta Math. 131 (1973) 207-248], this result implies that stationary solutions to multivariate linear stochastic recurrence equations are regularly varying. Since GARCH processes can be embedded in such recurrence equations their finite-dimensional distributions ar...
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作者：Jarner, SF; Roberts, GO
作者单位：Lancaster University
摘要：This paper considers the use of Foster-Liapounov-type drift conditions to establish polynomial rates of convergence of the f-norm for a general state space Markov chain in discrete time. Results of this type involving geometric convergence rates are now well established; see, for example, Meyn and Tweedie (11992) and Chapters 15, 16 of Meyn and Tweedie (1993). However, the more subtle polynomial case is not nearly as well understood. The foundational work of Tuominen and Tweedie (1994) studies...
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作者：Penrose, MD; Yukich, JE
作者单位：Durham University; Lehigh University
摘要：Consider sequential packing of unit balls in a large cube, as in the Renyi car-parking model, but in any dimension and with finite input. We prove a law of large numbers and central limit theorem for the number of packed balls in the thermodynamic limit. We prove analogous results for numerous related applied models, including cooperative sequential adsorption, ballistic deposition, and spatial birth-growth models. The proofs are based on a general law of large numbers and central limit theore...
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作者：Holroyd, AE
作者单位：University of California System; University of California Los Angeles
摘要：We study the effects of boundary conditions in two-dimensional rigidity percolation. Specifically, we consider generic rigidity in the bond percolation model on the triangular lattice. We introduce a theory of boundary conditions and define two different notions of ''rigid clusters,'' called r(0)-clusters and r(1)-clusters, which correspond to free boundary conditions and wired boundary conditions respectively. The definition of an r(0)-cluster turns out to be equivalent to the definition of a...
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作者：Mansfield, P; Rachev, ST; Samorodnitsky, G
作者单位：University of Tasmania; Cornell University; Cornell University; Cornell University; Helmholtz Association; Karlsruhe Institute of Technology
摘要：We study long strange intervals in a linear stationary stochastic process with regularly varying tails. It turns out that the length of the longest strange interval grows, as a function of the sample size, at different rates in different parts of the parameter space. We argue that this phenomenon may be viewed in a fruitful way as a phase transition between short- and long-range dependence, We prove a limit theorem that may form a basis for statistical detection of long-range dependence.
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作者：Mountford, T
作者单位：University of California System; University of California Los Angeles
摘要：We prove, using results for hydrodynamic limits, that an exclusion process starting from an ergodic initial distribution converges to product measure in one dimension. Our only assumption is the existence of a nonzero mean for the underlying random walk.
