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作者：Assaf, Sami; Diaconis, Persi; Soundararajan, K.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Stanford University
摘要：We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, for example, suits disregarded or only the colors of interest. For these features the number of shuffles drops from 3/2 log(2) n to log(2) n. We derive closed formulae and an asymptotic rule of thumb formula which is remarkably accurate.
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作者：Chatterjee, Sourav; Diaconis, Persi; Sly, Allan
作者单位：New York University; Stanford University; Microsoft
摘要：Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovasz and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. The argument proceeds by studying a natural exponential model having the degree sequence as a suffici...
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作者：Dereich, Steffen
作者单位：Philipps University Marburg
摘要：We introduce and analyze multilevel Monte Carlo algorithms for the, computation of E(f) (Y), where Y = (Y(t))t is an element of[0, 1] is the solution of a multidimensional Levy-driven stochastic differential equation and f is a real-valued function on the path space. The algorithm relies on approximations obtained by simulating large jumps of the Levy process individually and applying a Gaussian approximation for the small jump part. Upper bounds are provided for the worst case error over the ...
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作者：Chatterjee, Shirshendu; Durrett, Rick
作者单位：Cornell University; Duke University
摘要：Aldous [(2007) Preprint] defined a gossip process in which space is a discrete N x N torus, and the state of the process at time t is the set of individuals who know the information. Information spreads from a site to its nearest neighbors at rate 1/4 each and at rate N(-alpha) to a site chosen at random from the torus. We will be interested in the case in which alpha < 3, where the long range transmission significantly accelerates the time at which everyone knows the information. We prove thr...
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作者：Chen, Xinfu; Cheng, Lan; Chadam, John; Saunders, David
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh; State University of New York (SUNY) System; SUNY Fredonia; University of Waterloo
摘要：We study the inverse boundary crossing problem for diffusions. Given a diffusion process X-t, and a survival distribution p on [0,8), we demonstrate that there exists a boundary b(t) such that p(t) = P [tau > t], where t is the first hitting time of X-t to the boundary b(t). The approach taken is analytic, based on solving a parabolic variational inequality to find b. Existence and uniqueness of the solution to this variational inequality were proven in earlier work. In this paper, we demonstr...
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作者：Shkolnikov, Mykhaylo
作者单位：Stanford University
摘要：We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. Levy processes endowed with rank-dependent drift and diffusion coefficients. In the finite systems we show that the processes of gaps in the respective particle configurations possess unique invariant distributions and prove the convergence of the gap processes to the latter in the total variation distance, assuming a bound on the jumps of ...
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作者：Cuchiero, Christa; Filipovic, Damir; Mayerhofer, Eberhard; Teichmann, Josef
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Swiss Finance Institute (SFI)
摘要：This article provides the mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. This analysis has been motivated by a large and growing use of matrix-valued affine processes in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities.
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作者：Taflin, Erik
作者单位：CY Cergy Paris Universite; Ecole Internationale des Sciences du Traitement de linformation; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We construct Zero-Coupon Bond markets driven by a cylindrical Brownian motion in which the notion of generalized portfolio has important flaws: There exist bounded smooth random variables with generalized hedging portfolios for which the price of their risky part is +infinity at each time. For these generalized portfolios, sequences of the prices of the risky part of approximating portfolios can be made to converges to any given extended real number in [-infinity, infinity].
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作者：Como, Giacomo; Fagnani, Fabio
作者单位：Massachusetts Institute of Technology (MIT); Polytechnic University of Turin
摘要：Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary diff...
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作者：Hairer, Martin; Stuart, Andrew M.; Voss, Jochen
作者单位：University of Warwick; University of Leeds
摘要：A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of elliptic diffusions where the drift has a gradient structure and the resulting SPDE is of second-order parabolic type. The present article extends this methodology to allow the construction of SPDEs which are invariant with respect to the distribution of a c...
