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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.
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作者：Benjamini, Itai; Nachmias, Asaf; Peres, Yuval
作者单位：Weizmann Institute of Science; Microsoft
摘要：We show that the critical probability for percolation on a d-regular non-amenable graph of large girth is close to the critical probability for percolation on an infinite d-regular tree. We also prove a finite analogue of this statement, valid for expander graphs, without any girth assumption.
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作者：Vershynin, Roman
作者单位：University of Michigan System; University of Michigan
摘要：We study the spectral norm of matrices W that can be factored as W = BA, where A is a random matrix with independent mean zero entries and B is a fixed matrix. Under the (4 + epsilon)th moment assumption on the entries of A, we show that the spectral norm of such an m x n matrix W is bounded by root m + root n, which is sharp. In other words, in regard to the spectral norm, products of random and deterministic matrices behave similarly to random matrices with independent entries. This result a...
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作者：Bassetti, Federico; Ladelli, Lucia; Matthes, Daniel
作者单位：Polytechnic University of Milan; University of Pavia; Technische Universitat Wien
摘要：We introduce a class of kinetic-type equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with rather general properties. By establishing a connection to the central limit problem, we are able to prove long-time convergence of the equation's solutions toward a limit distribution. For example, we prove that if the initial condition belongs to the domain of normal attraction of a certain s...
