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作者：Diehl, Joscha; Friz, Peter
作者单位：Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Lecture Notes in Control and Inform. Sci. 176 (1992) 200-217] provide a non-Markovian extension to certain classes of nonlinear partial differentia] equations; the nonlinearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in time. To this end, we establish continuity of BSDE solutions with respect to rough path metrics in the sense of Lyons [Re...
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作者：Miller, Jason; Peres, Yuval
作者单位：Stanford University; Microsoft
摘要：We show that the measure on markings of Z(n)(d), d >= 3, with elements of {0, 1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1/2 T-cov (Z(n)(d)). a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter graph Z(2) (sic) Z(n)(d), d >= 3, has a cutoff with threshold 1/2 T-cov (Z(n)(d)). We give a ge...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：Let B-s be a d-dimensional Brownian motion and omega(dx) be an independent Poisson field on R-d. The almost sure asymptotics for the logarithmic moment generating function logE(0) exp{+/-theta integral(t)(0)(V) over bar (B-s)ds} (t -> infinity) are investigated in connection with the renormalized Poisson potential of the form (V) over bar (x) = integral(Rd) 1/vertical bar y - x vertical bar(p)[omega(dy) - dy], x is an element of R-d. The investigation is motivated by some practical problems ar...
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作者：Hammond, Alan
作者单位：University of Oxford
摘要：We study the droplet that results from conditioning the planar subcritical Fortuin-Kasteleyn random cluster model on the presence of an open circuit Gamma(0) encircling the origin and enclosing an area of at least (or exactly) n(2). We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR(Gamma(0)), this being the maximum distance from a point in the circuit Gamma(0) to the boundary a conv(Gamma(0)) of the circuit's convex hull; and in...
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作者：Hu, Yaozhong; Lu, Fei; Nualarti, David
作者单位：University of Kansas
摘要：In this paper, a Feynman-Kac formula is established for stochastic partial differential equation driven by Gaussian noise which is, with respect to time, a fractional Brownian motion with Hurst parameter H < 1/2. To establish such a formula, we introduce and study a nonlinear stochastic integral from the given Gaussian noise. To show the Feynman-Kac integral exists, one still needs to show the exponential integrability of nonlinear stochastic integral. Then, the approach of approximation with ...
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作者：Kolb, Martin; Steinsaltz, David
作者单位：University of Oxford
摘要：This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285-1234], which found conditions for convergence of a killed one-dimensional diffusion conditioned on survival, to a quasistationary distribution whose density is given by the principal eigenfunction of the generator. Under the assumption that the limit of the killing at infinity differs from the principal eigenvalue we prove that convergence to quasistationarity occurs if and only if the pri...
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作者：Tao, Terence; Vu, Van
作者单位：University of California System; University of California Los Angeles; Rutgers University System; Rutgers University New Brunswick
摘要：We study the eigenvalues of the covariance matrix 1/n M*M of a large rectangular matrix M = M-n,M-p = (zeta(ij))(1 <= i <= p;1 <= j <= n) whose entries are i.i.d. random variables of mean zero, variance one, and having finite C(0)th moment for some sufficiently large constant C-0. The main result of this paper is a Four Moment theorem for i.i.d. covariance matrices (analogous to the Four Moment theorem for Wigner matrices established by the authors in [Acta Math. (2011) Random matrices: Univer...
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作者：Carraro, Laurent; El Karoui, Nicole; Obloj, Jan
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; University of Oxford
摘要：We study the class of Azema-Yor processes defined from a general semi-martingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown property: they always stay above a given function of their past maximum. We then show that any process which satisfies the drawdown property is in fact an Azema-Yor process. Th...
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作者：Pitman, Jim; Bravo, Geronimo Uribe
作者单位：University of California System; University of California Berkeley
摘要：We offer a unified approach to the theory of convex minorants of Levy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a Levy process on both finite and infinite time intervals, and of a Poisson point process of excursions above the convex minorant up to an independent exponential time. The Poisson Dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a Levy process with cont...
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作者：Damron, Michael; Sapozhnikov, Artem
作者单位：Princeton University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the nth of which gives the number of outlets in the box centered at the origin of side length 2(n). The most important of these properties describes the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers ...
