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作者：Bovier, Anton; Gayrard, Veronique
作者单位：University of Bonn; Aix-Marseille Universite
摘要：We derive a general criterion for the convergence of clock processes in random dynamics in random environments that is applicable in cases when correlations are not negligible, extending recent results by Gayrard [(2010), (2011), forthcoming], based on general criterion for convergence of sums of dependent random variables due to Durrett and Resnick [Ann. Probab. 6 (1978) 829-846]. We demonstrate the power of this criterion by applying it to the case of random hopping time dynamics of the p-sp...
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作者：Auffinger, Antonio; Ben Arous, Gerard
作者单位：University of Chicago; New York University
摘要：We analyze the landscape of general smooth Gaussian functions on the sphere in dimension N, when N is large. We give an explicit formula for the asymptotic complexity of the mean number of critical points of finite and diverging index at any level of energy and for the mean Euler characteristic of level sets. We then find two possible scenarios for the bottom landscape, one that has a layered structure of critical values and a strong correlation between indexes and critical values and another ...
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作者：Ledrappier, Francois
作者单位：University of Notre Dame; Sorbonne Universite
摘要：We consider nondegenerate, finitely supported random walks on a finitely generated Gromov hyperbolic group. We show that the entropy and the escape rate are Lipschitz functions of the probability if the support remains constant.
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作者：Gloter, Arnaud; Martinez, Miguel
作者单位：Universite Paris Saclay; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we consider two skew Brownian motions, driven by the same Brownian motion, with different starting points and different skewness coefficients. We show that we can describe the evolution of the distance between the two processes with a stochastic differential equation. This S.D.E. possesses a jump component driven by the excursion process of one of the two skew Brownian motions. Using this representation, we show that the local time of two skew Brownian motions at their first hit...
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作者：Drapeau, Samuel; Heyne, Gregor; Kupper, Michael
作者单位：Humboldt University of Berlin
摘要：We study the nonlinear operator of mapping the terminal value xi to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in y, convex in z, jointly lower semicontinuous and bounded below by an affine function of the control variable z. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.
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作者：Lee, James R.; Peres, Yuval
作者单位：University of Washington; University of Washington Seattle; Microsoft
摘要：We prove diffusive lower bounds on the rate of escape of the random walk on infinite transitive graphs. Similar estimates hold for finite graphs, up to the relaxation time of the walk. Our approach uses nonconstant equivariant harmonic mappings taking values in a Hilbert space. For the special case of discrete, amenable groups, we present a more explicit proof of the Mok-Korevaar-Schoen theorem on the existence of such harmonic maps by constructing them from the heat flow on a Folner set.
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作者：Lawler, Gregory F.; Zhou, Wang
作者单位：University of Chicago; National University of Singapore
摘要：Developing the theory of two-sided radial and chordal SLE, we prove that the natural parametrization on SLE kappa curves is well defined for all kappa <8. Our proof uses a two-interior-point local martingale.
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作者：Gill, Hardeep
作者单位：University of British Columbia
摘要：We construct a supercritical interacting measure-valued diffusion with representative particles that are attracted to, or repelled from, the center of mass. Using the historical stochastic calculus of Perkins, we modify a super Ornstein-Uhlenbeck process with attraction to its origin, and prove continuum analogues of results of Englander [Electron. J. Probab. 15 (2010) 1938-1970] for binary branching Brownian motion. It is shown, on the survival set, that in the attractive case the mass normal...
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作者：Ivanov, Alexander V.; Leonenko, Nikolai; Ruiz-Medina, Maria D.; Savich, Irina N.
作者单位：Ministry of Education & Science of Ukraine; Igor Sikorsky Kyiv Polytechnic Institute; Cardiff University; University of Granada
摘要：The limit Gaussian distribution of multivariate weighted functionals of nonlinear transformations of Gaussian stationary processes, having multiple singular spectra, is derived, under very general conditions on the weight function. This paper is motivated by its potential applications in nonlinear regression, and asymptotic inference on nonlinear functionals of Gaussian stationary processes with singular spectra.
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作者：Pene, Francoise; Saussol, Benoit; Zweimueller, Roland
作者单位：Universite de Bretagne Occidentale; University of Vienna
摘要：We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as epsilon -> 0, of the return time to (-epsilon, epsilon). We then refine this result by establishing a limit theorem for the hitting-time distributions of (x - epsilon, x + epsilon) with arbitrary x is an element of R.
