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作者：GOROSTIZA, LG; ROELLY, S; WAKOLBINGER, A
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Johannes Kepler University Linz
摘要：We consider a class of systems of particles of k types in R(d) undergoing spatiai diffusion and critical multitype branching, where the diffusions, the particle lifetimes and the branching laws depend on the types. We prove persistence criteria for such systems and for their corresponding high density limits known as multitype Dawson-Watanabe processes. The main tool is a representation of the Palm distributions for a general class of inhomogeneous critical branching particle systems, construc...
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作者：PERMAN, M; PITMAN, J; YOR, M
作者单位：Sorbonne Universite; University of California System; University of California Berkeley
摘要：Some general formulae are obtained for size-biased sampling from a Poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function. These formulae explain why in certain cases (gamma and stable) the size-biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking (residual allocation) scheme defined by independent beta random variables. An application is made to length biased sampling of excursion...
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作者：YOSHIDA, N
摘要：The asymptotic expansions of the probability distributions of statistics for the small diffusion are derived by means of the Malliavin calculus. From this the second order efficiency of the maximum likelihood estimator is proved.
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作者：HALL, P; MARRON, JS; PARK, BU
作者单位：Seoul National University (SNU)
摘要：For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be be...
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作者：VUOLLEAPIALA, J
摘要：Let (X(t), P(x)) be a rotation invariant (RI) strong Markov process on R(d)\{0} having a skew product representation [\X(t)\, theta(At)], where (theta(t)) is a time homogeneous, RI strong Markov process on S(d-1), \X(t)\ and theta(t) are independent under P(x) and A(t) is a continuous additive functional of \X(t)\. We characterize the rotation invariant extensions of (X(t), P(x)) to R(d). Two examples are given: the diffusion case, where especially the Walsh's Brownian motion (Brownian hedgeho...
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作者：GREVEN, A; DENHOLLANDER, F
作者单位：Utrecht University
摘要：Let (eta(n)) be the infinite particle system on Z whose evolution is as follows. At each unit of time each particle independently is replaced by a new generation. The size of a new generation descending from a particle at site x has distribution F(x) and each of its members independently jumps to site x +/- 1 with probability (1 +/- h)/2, h is-an-element-of [0, 1]. The sequence {F(x)} is i.i.d. with uniformly bounded second moment and is kept fixed during the evolution. The initial configurati...
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作者：RACHEV, ST; RUSCHENDORF, L
作者单位：University of Munster
摘要：A new ideal metric of order r > 1 is introduced on R(k) and a thorough analysis of its metric properties is given. In comparison to the known ideal metric of Zolotarev this new metric allows estimates from above by pseudo difference moments and thus allows applications to stable limit theorems. As applications we give the right order Berry-Esseen type result in the stable case, obtain the limiting behaviour of multivariate summability methods and discuss the approximation problem by compound P...
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作者：MAMMEN, E; MARRON, JS; FISHER, NI
作者单位：Commonwealth Scientific & Industrial Research Organisation (CSIRO); University of North Carolina; University of North Carolina Chapel Hill
摘要：A test due to B.W. Silverman for modality of a probability density is based on counting modes of a kernel density estimator, and the idea of critical smoothing. An asymptotic formula is given for the expected number of modes. This, together with other methods, establishes the rate of convergence of the critically smoothed bandwidth. These ideas are extended to provide insight concerning the behaviour of the test based on bootstrap critical values.
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作者：PERKINS, E
摘要：A strong equation driven by a historical Brownian motion is used to construct and characterize measure-valued branching diffusions in which the spatial motions obey an Ito equation with drift and diffusion depending on the position of an individual and the entire population.
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作者：GANDOLFI, A; KEANE, MS; NEWMAN, CM
作者单位：New York University; Delft University of Technology
摘要：We extend the theorem of Burton and Keane on uniqueness of the infinite component in dependent percolation to cover random graphs on Z(d) or Z(d) x N with long-range edges. We also study a short-range percolation model related to nearest-neighbor spin glasses on Z(d) or on a slab Z(d) x {0,..., K} and prove both that percolation occurs and that the infinite component is unique for V = Z2 x {0,1} or larger.
