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作者：Durrett, Rick; Remenik, Daniel
作者单位：Duke University; University of Toronto
摘要：We consider a branching-selection system in R with N particles which give birth independently at rate 1 and where after each birth the leftmost particle is erased, keeping the number of particles constant. We show that, as N -> 8, the empirical measure process associated to the system converges in distribution to a deterministic measure-valued process whose densities solve a free boundary integro-differential equation. We also show that this equation has a unique traveling wave solution travel...
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作者：Crane, Edward; Georgiou, Nicholas; Volkov, Stanislav; Wade, Andrew R.; Waters, Robert J.
作者单位：University of Bristol; University of Strathclyde
摘要：We study a generalized Polya urn model with two types of ball. If the drawn ball is red, it is replaced together with a black ball, but if the drawn ball is black it is replaced and a red ball is thrown out of the urn. When only black balls remain, the roles of the colors are swapped and the process restarts. We prove that the resulting Markov chain is transient but that if we throw out a ball every time the colors swap, the process is recurrent. We show that the embedded process obtained by o...
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作者：Goldenshluger, Alexander; Lepski, Oleg
作者单位：University of Haifa; Aix-Marseille Universite
摘要：In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the L-s-norms of empirical and regression-type processes. Usefulness of the obtained results is illustrated by application to the processes appearing in kernel density estimation and in nonparametric estimation of regression functions.
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作者：Applebaum, David
作者单位：University of Sheffield
摘要：We introduce a class of central symmetric infinitely divisible probability measures on compact Lie groups by lifting the characteristic exponent from the real line via the Casimir operator. The class includes Gauss, Laplace and stable-type measures. We find conditions for such a measure to have a smooth density and give examples. The Hunt semigroup and generator of convolution semigroups of measures are represented as pseudo-differential operators. For sufficiently regular convolution semigrou...
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作者：Benaim, Michel; Tarres, Pierre
作者单位：University of Neuchatel; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We generalize a result from Volkov [Ann. Probab. 29 (2001) 66-91] and prove that, on a large class of locally finite connected graphs of bounded degree (G, similar to)and symmetric reinforcement matrices a = (a(i), (j))(i),(j is an element of G), the vertex-reinforced random walk (VRRW) eventually localizes with positive probability on subsets which consist of a complete d-partite subgraph with possible loops plus its outer boundary. We first show that, in general, any stable equilibrium of a ...
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作者：Bernyk, Violetta; Dalang, Robert C.; Peskir, Goran
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; University of Manchester
摘要：Given a stable Levy process X = (X-t)(0 <= t <= T) of index alpha is an element of (1, 2) with no negative jumps, and letting S-t = sup(0 <= s <= t) X-s denote its running supremum for t is an element of [0, T], we consider the optimal prediction problem V = inf(0 <=tau <= T) E(S-T - X-tau)(p), where the infimum is taken over all stopping times tau of X, and the error parameter p is an element of(1, alpha) is given and fixed. Reducing the optimal prediction problem to a fractional free-boundar...
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作者：Beiglboeck, Mathias; Schachermayer, Walter; Veliyev, Bezirgen
作者单位：University of Vienna
摘要：We give an elementary proof of the celebrated Bichteler-Dellacherie theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S = M + A, where M is a local martingale and A is a finite variation process. In other words, S is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposit...
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作者：Castell, Fabienne; Guillotin-Plantard, Nadine; Pene, Francoise; Schapira, Bruno
作者单位：Aix-Marseille Universite; 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); Centre National de la Recherche Scientifique (CNRS); Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Random walks in random scenery are processes defined by Z(n) := Sigma(n)(k) = 1 X-xi(1)+... + X-k, where (X-k, k >= 1) and (xi(y), y is an element of Z) are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index alpha is an element of (0, 2] and beta is an element of (0, 2], respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved the convergence in distrib...
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作者：Curien, Nicolas; Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those chords that do not intersect the previous ones. After throwing infinitely many chords and taking the closure of the resulting set, one gets a random compact subset of the unit disk whose complement is a countable union of triangles. We show that this limiting ...
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作者：Berkes, Istvan; Hormann, Siegfried; Schauer, Johannes
作者单位：Graz University of Technology; Universite Libre de Bruxelles
摘要：The results of Komlos, Major and Tusnady give optimal Wiener approximation of partial sums of i.i.d. random variables and provide an extremely powerful tool in probability and statistical inference. Recently Wu [Ann. Probab. 35 (2007) 2294-2320] obtained Wiener approximation of a class of dependent stationary processes with finite pth moments, 2 < p <= 4, with error term o(n(1/p)(log n)(gamma)), gamma > 0, and Liu and Lin [Stochastic Process. Appl. 119 (2009) 249-280] removed the logarithmic f...
