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作者：Lijoi, A; Regazzini, E
作者单位：University of Pavia; University of Pavia
摘要：The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and the parameter of a Dirichlet process, a characterization of the family of Cauchy distributions as the...
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作者：Külske, C; Le Ny, A; Redig, F
作者单位：Technical University of Berlin; Universite Paris Saclay; Eindhoven University of Technology
摘要：We study the relative entropy density for generalized Gibbs measures. We first show its existence and obtain a familiar expression in terms of entropy and relative energy for a class of almost Gibbsian measures (almost sure continuity of conditional probabilities). For quasilocal measures, we obtain a full variational principle. For the joint measures of the random field Ising model, we show that the weak Gibbs property holds, with an almost surely rapidly decaying translation-invariant potent...
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作者：Funaki, T
作者单位：University of Tokyo
摘要：We consider a system of interacting Brownian particles in R-d with a pairwise potential, which is radially symmetric, of finite range and attains a unique minimum when the distance of two particles becomes a > 0. The asymptotic behavior of the system is studied under the zero temperature limit from both microscopic and macroscopic aspects. If the system is rigidly crystallized, namely if the particles are rigidly arranged in an equal distance a, the crystallization is kept under the evolution ...
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作者：Iksanov, AM; Jurek, ZJ; Schreiber, BM
作者单位：Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; University of Wroclaw
摘要：We prove that the convolution of a selfdecomposable distribution with its background driving law is again selfdecomposable if and only if the background driving law is s-selfdecomposable. We will refer to this as the factorization property of a selfdecomposable distribution; let L-f denote the set of all these distributions. The algebraic structure and various characterizations of L-f are studied. Some examples are discussed, the most interesting one being given by the Levy stochastic area int...
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作者：Le Jan, Y; Raimond, O
作者单位：Universite Paris Saclay
摘要：We are interested in stationary fluid random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE ...
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作者：Luschgy, H; Pagès, G
作者单位：Universitat Trier; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：The sharp asymptotics for the L-2-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.
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作者：Bentkus, V
作者单位：Vilnius University; Vytautas Magnus University
摘要：In a celebrated work by Hoeffding [J. Amer Statist. Assoc. 58 (1963) 13-30], several inequalities for tail probabilities of sums Mn = X-1 +... + X-n of bounded independent random variables X-j were proved. These inequalities had a considerable impact on the development of probability and statistics, and remained unimproved until 1995 when Talagrand [Inst. Hautes Etudes Sci. Publ. Math. 81 (1995a) 73-205] inserted certain missing factors in the bounds of two theorems. By similar factors, a thir...
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作者：Houdré, C; Marchal, P
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); University System of Georgia; Georgia Institute of Technology; Universite PSL; Ecole Normale Superieure (ENS)
摘要：Concentration of measure is studied, and obtained, for stable and related random vectors.
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作者：Doney, RA
作者单位：University of Manchester
摘要：Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks have the same step distribution, but different random starting points. In principle, this allows one to deduce Levy process versions of many known results about the large-time behavior of random walks. This is illustrated by establishing a comprehensive theorem about Levy processes which converge to infinity in probabi...
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作者：Samorodnitsky, G
作者单位：Cornell University
摘要：We study the partial maxima of stationary alpha-stable processes. We relate their asymptotic behavior to the ergodic theoretical properties of the flow. We observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative, and argue that this may indicate a change from a short memory process to a long memory process.
