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作者：Brunick, Gerard
作者单位：University of California System; University of California Santa Barbara
摘要：We study the martingale problem associated with the operator Lu(s, x) = partial derivative(s)u(s, x) + 1/2 Sigma(d0)(i,j=1) a(ij)(s, x)partial derivative(ij)u(s, x) + Sigma(d)(i,j=1) B(ij)x(j)partial derivative(i)u(s, x), where d(0) < d. We show that the martingale problem is well-posed when the function a is continuous and strictly positive definite on R-d0 and the matrix B takes a particular lower-diagonal, block form. We then localize this result to show that the martingale problem remains ...
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作者：Hammond, Alan; Sheffield, Scott
作者单位：University of Oxford; Massachusetts Institute of Technology (MIT)
摘要：We introduce a natural family of random walks S-n on Z that scale to fractional Brownian motion. The increments X-n := S-n - Sn-1 is an element of {+/- 1} have the property that given {X-k : k < n}, the conditional law of X-n is that of Xn-kn, where k(n) is sampled independently from a fixed law mu on the positive integers. When mu has a roughly power law decay (precisely, when mu lies in the domain of attraction of an alpha-stable subordinator, for 0 < alpha < 1/2) the walks scale to fraction...
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作者：del Barrio, Eustasio; Matran, Carlos
作者单位：Universidad de Valladolid
摘要：We consider a class of partial mass problems in which a fraction of the mass of a probability measure is allowed to be changed (trimmed) to maximize fit to a given pattern. This includes the problem of optimal partial transportation of mass, where a part of the mass need not be transported, and also trimming procedures which are often used in statistical data analysis to discard outliers in a sample (the data with lowest agreement to a certain pattern). This results in a modified, trimmed vers...
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作者：Quastel, Jeremy; Remenik, Daniel
作者单位：University of Toronto; Universidad de Chile
摘要：We obtain a formula for the -dimensional distributions of the process in terms of a Fredholm determinant on , as opposed to the standard formula which involves extended kernels, on . The formula is analogous to an earlier formula of Prahofer and Spohn (J Stat Phys 108(5-6):1071-1106, 2002) for the process. Using this formula we are able to prove that the process is Holder continuous with exponent -and that it fluctuates locally like a Brownian motion. We also explain how the same methods can b...
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作者：Ichiba, Tomoyuki; Karatzas, Ioannis; Shkolnikov, Mykhaylo
作者单位：University of California System; University of California Santa Barbara; Columbia University
摘要：We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We show that strong existence and uniqueness hold until the first time three particles collide. Motivated by this result, we improve significantly the existing conditions for the absence of such triple collisions in the case of finite-dimensional systems, and pr...
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作者：Fernholz, E. Robert; Ichiba, Tomoyuki; Karatzas, Ioannis; Prokaj, Vilmos
作者单位：University of California System; University of California Santa Barbara; Columbia University; Eotvos Lorand University; Hungarian Academy of Sciences; HUN-REN; HUN-REN Institute for Computer Science & Control
摘要：For given nonnegative constants g, h, rho, sigma with rho(2)+sigma(2) = 1 and g+h > 0, we construct a diffusion process (X-1(center dot), X-2(center dot)) with values in the plane and infinitesimal generator L=1({x1>x2})(rho(2)/2 alpha(2)/alpha x12+sigma(2)/2 alpha(2)/alpha x22-h alpha/alpha x1+g alpha/alpha x2) +1({x1>x2})(sigma(2)/2 alpha(2)/alpha x12+rho(2)/2 alpha(2)/alpha x22 + g alpha/alpha x1-h alpha/alpha x2), (0.1) and discuss its realization in terms of appropriate systems of stochas...
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作者：Benjamini, Itai; Gurel-Gurevich, Ori; Morris, Ben
作者单位：Weizmann Institute of Science; University of British Columbia; University of California System; University of California Davis
摘要：We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. We conjecture that the same holds for any simple graph.
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作者：van Handel, Ramon
作者单位：Princeton University
摘要：Let F be a separable uniformly bounded family of measurable functions on a standard measurable space (X, X, and let N-[](F, epsilon, mu) be the smallest number of epsilon-brackets in L-1(mu) needed to cover F. The following are equivalent: F is a universal Glivenko-Cantelli class. N-[](F, epsilon, mu) < infinity for every epsilon > 0 and every probability measure mu. F is totally bounded in L-1(mu) for every probability measure mu. F does not contain a Boolean sigma-independent sequence. It fo...
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作者：Bordenave, Charles; Lelarge, Marc; Salez, Justin
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Cite
摘要：Elek and Lippner (Proc. Am. Math. Soc. 138(8), 2939-2947, 2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting parameter via a local recursion defined directly on the limit of the graph sequence. Interestingly, the recursion may admit multiple solutions, implying non-trivial long-range dependencies between the covered vertices. We over...
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作者：Bull, Adam D.; Nickl, Richard
作者单位：University of Cambridge
摘要：The problem of constructing confidence sets that are adaptive in -loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev ball and its smoothness degree, and over maximal parameter spaces for which adaptation is possible. Two key regimes of parameter constellations are identified: one where full adaptation is possible, and one where adaptation requires critical regions be removed. T...
