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作者：El Karoui, Mcole; Meziou, Asma
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are concerned with a new type of supermartingale decomposition in the Max-Plus algebra, which essentially consists in expressing any supermartingale of class (D) as a conditional expectation of some running supremum process. As an application, we show how the Max-Plus supermartingale decomposition allows, in particular, to solve the American optimal stopping problem without having to compute the option price. Some illustrative examples based on one-dimensional diffusion processes are then p...
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作者：Varadhan, S. R. S.
作者单位：New York University
摘要：This paper is based oil Wald Lectures given at the annual meeting of the IMS in Minneapolis during August 2005. It is a survey of the theory of large deviations.
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作者：Marcus, Michael B.; Rosen, Jay
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：Let X = {X(t), t epsilon R+} be a real-valued symmetric Levy process with local times {L-t(x), (t, X) epsilon R+ x R} and characteristic function e(i lambda X(t)) = et(-t psi(lambda)). Let sigma(2)(0)(x-y) = 4/pi integral(infinity)(0) sin(2)(lambda(x-y)/2)/psi(lambda) d lambda. If sigma(2)(0)(h) is concave, and satisfies some additional very weak regularity conditions, then for any p >= t and all t epsilon R+, lim(h down arrow 0)integral(b)(a)vertical bar L-t(x+h) - L-t(x)/sigma(0)(h)vertical ...
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作者：Angel, Omer; Goodman, Jesse; Den Hollander, Frank; Slade, Gordon
作者单位：University of Toronto; University of British Columbia; Leiden University; Leiden University - Excl LUMC
摘要：We consider invasion percolation on a rooted regular tree. For the infinite cluster invaded from the root, we identify the scaling behavior of its r-point function for any r >= 2 and of its volume both at a given height and below a given height. We find that while the power laws of the scaling are the same as for the incipient infinite cluster for ordinary percolation, the scaling functions differ. Thus, somewhat surprisingly, the two clusters behave differently; in fact, we prove that their l...
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作者：Burdzy, Krzysztof; Chen, Zhen-Qing
作者单位：University of Washington; University of Washington Seattle
摘要：In this paper we investigate three discrete or semi-discrete approximation schemes for reflected Brownian motion on bounded Euclidean domains. For a class of bounded domains D in R-n that includes all bounded Lipschitz domains and the von Koch snowflake domain, we show that the laws of both discrete and continuous time simple random walks on D boolean AND 2(-k)Z(n) moving at the rate 2(-2k) with stationary initial distribution converge weakly in the space D([0, 1], R-n), equipped with the Skor...
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作者：Jonasson, Johan; Steif, Jeffrey E.
作者单位：Chalmers University of Technology; University of Gothenburg
摘要：We consider two dynamical variants of Dvoretzky's classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length C is updated at rate l(-a) where alpha >= 0 is a parameter. For the model with Brownian motions, a spe...
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作者：Bryc, Wlodzimierz; Matysiak, Wojciech; Wesolowski, Jacek
作者单位：University System of Ohio; University of Cincinnati; Warsaw University of Technology
摘要：This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam-Chihara polynomials and a relation between these polynomials for different values of parameters.
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作者：Sole, Josep Lluis; Utzet, Frederic
作者单位：Autonomous University of Barcelona
摘要：Let X = {X-t, t >= 0} be a cadlag Levy process, centered, with moments of all orders. There are two families of orthogonal polynomials associated with X. On one hand, the Kailath-Segall formula gives the relationship between the iterated integrals and the variations of order n of X, and defines a family of polynomials P-1(x(t)), P-2(x(1), x(2)).... that are orthogonal with respect to the joint law of the variations of X. On the other hand, we can F construct a sequence of orthogonal polynomial...
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作者：Zhan, Dapeng
作者单位：Yale University
摘要：We define a family of stochastic Loewner evolution-type processes in finitely connected domains, which are called continuous LERW (loop-erased random walk). A continuous LERW describes a random curve in a finitely connected domain that starts from a prime end and ends at a certain target set, which could be an interior point, or a prime end, or a side arc. It is defined using the usual chordal Loewner equation with the driving function being root 2B(t) plus a drift term. The distributions of c...
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作者：Berger, Noam
作者单位：University of California System; University of California Los Angeles
摘要：We show that random walk in uniformly elliptic i.i.d. environment in dimension >= 5 has at most one non zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes connections between different conjectures.
