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作者：Buchmann, Boris; Maller, Ross
作者单位：Monash University; Australian National University
摘要：We give a small time functional version of Chung's other law of the iterated logarithm for L,vy processes with non-vanishing Brownian component. This is an analogue of the other law of the iterated logarithm at large times for L,vy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.
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作者：Baraud, Yannick
作者单位：Universite Cote d'Azur
摘要：We observe a random measure N and aim at estimating its intensity s. This statistical framework allows to deal simultaneously with the problems of estimating a density, the marginals of a multivariate distribution, the mean of a random vector with nonnegative components and the intensity of a Poisson process. Our estimation strategy is based on estimator selection. Given a family of estimators of s based on the observation of N, we propose a selection rule, based on N as well, in view of selec...
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作者：Nandori, Peter
作者单位：Budapest University of Technology & Economics
摘要：In the classical paper of Dvoretzky and ErdAs (Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, pp 353-367, 1951), asymptotics for the expected value and the variance of the number of distinct sites visited by a Simple Symmetric Random Walk were calculated. Here, these results are generalized for Random Walks with Internal States. Moreover, both weak and strong laws of large numbers are proved. As a tool for these results, the error term of the local limit ...
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作者：Rohde, Angelika
作者单位：University of Hamburg
摘要：Based on two independent samples X (1), . . . , X (m) and X (m+1), . . . , X (n) drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of significant deviations between p and q. The construction is built from randomized nearest-neighbor statistics. It does not require any preliminary information about the multivariate densities such as compact support, strict positivity or smooth...
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作者：Frei, Christoph; Malamud, Semyon; Schweizer, Martin
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Institut Polytechnique de Paris; Ecole Polytechnique; Swiss Finance Institute (SFI); Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider backward stochastic differential equations (BSDEs) with a particular quadratic generator and study the behaviour of their solutions when the probability measure is changed, the filtration is shrunk, or the underlying probability space is transformed. Our main results are upper bounds for the solutions of the original BSDEs in terms of solutions to other BSDEs which are easier to solve. We illustrate our results by applying them to exponential utility indifference valuation in a mul...
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Let G be a measurable group with Haar measure., acting properly on a space S and measurably on a space T. Then any sigma-finite, jointly invariant measure M on S x T admits a disintegration nu circle times mu into an invariant measure nu on S and an invariant kernel mu from S to T. Here we construct nu and mu by a general skew factorization, which extends an approach by Rother and Zahle for homogeneous spaces S over G. This leads to easy extensions of some classical propositions for invariant ...
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作者：Sabot, Christophe
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We consider random walks in random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On Z(d), RWDE are parameterized by a 2d-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension d >= 3. We also prove that the Green function has some finite moments and we characterize the finite moments. Our result is more general and appli...
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作者：Last, Guenter; Penrose, Mathew D.
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath
摘要：We consider a Poisson process eta on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of eta. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-It chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincar, ineq...
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作者：Bouleau, Nicolas; Denis, Laurent
作者单位：Universite Paris Saclay; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We apply the Dirichlet form theory to stochastic differential equations with jumps as extension of Malliavin calculus reasoning. As in the continuous case, this weakens significantly the assumptions on the coefficients of the SDE. Thanks to the flexibility of the Dirichlet forms language, this approach brings also an important simplification which was neither available nor visible previously: an explicit formula giving the carr, du champ matrix, i.e., the Malliavin matrix. Following this formu...
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作者：Hug, Daniel; Schneider, Rolf
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Freiburg
摘要：For a stationary Poisson-Voronoi tessellation in Euclidean d-space and for k is an element of {1, ... , d}, we consider the typical k-dimensional face with respect to a natural centre function. We express the distribution of this typical k-face in terms of a certain Poisson process of closed halfspaces in a k-dimensional space. Then we show that, under the condition of large inradius, the relative boundary of the typical k-face lies, with high probability, in a narrow spherical annulus.
