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作者：Hobson, David
作者单位：University of Warwick
摘要：Given the univariate marginals of a real-valued, continuous-time martingale, (resp., a family of measures parameterised by t is an element of [0, T] which is increasing in convex order, or a double continuum of call prices), we construct a family of pure jump martingales which mimic that martingale (resp., are consistent with the family of measures, or call prices). As an example, we construct a fake Brownian motion. Then, under a further dispersion assumption, we construct the martingale whic...
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作者：van der Hofstad, Remco; Holmes, Mark; Kuznetsov, Alexey; Ruszel, Wioletta
作者单位：Eindhoven University of Technology; University of Auckland; York University - Canada; Delft University of Technology
摘要：We introduce a class of reinforcement models where, at each time step t, one first chooses a random subset A(t) of colours (independently of the past) from n colours of balls, and then chooses a colour i from this subset with probability proportional to the number of balls of colour i in the urn raised to the power alpha > 1. We consider stability of equilibria for such models and establish the existence of phase transitions in a number of examples, including when the colours are the edges of ...
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作者：Sabanis, Sotirios
作者单位：University of Edinburgh
摘要：A new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these explicit schemes converge in probability and in L-P to the solution of the corresponding SDEs. Moreover, rate of convergence estimates are provided for L-P and almost sure convergence. In particular, the strong order 1/2 is recovered in the case of uniform L...
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作者：Cetin, Umut; Danilova, Albina
作者单位：University of London; London School Economics & Political Science
摘要：This paper develops a new methodology for studying continuous-time Nash equilibrium in a financial market with asymmetrically informed agents. This approach allows us to lift the restriction of risk neutrality imposed on market makers by the current literature. It turns out that, when the market makers are risk averse, the optimal strategies of the agents are solutions of a forward backward system of partial and stochastic differential equations. In particular, the price set by the market make...
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作者：Fang, Xiao; Siegmund, David
作者单位：National University of Singapore; Stanford University
摘要：As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables subject to possible change-points. Our formulation deals simultaneously with ordinary and with large deviations.
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作者：Verloop, I. M.
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National Polytechnique de Toulouse; Universite Toulouse III - Paul Sabatier
摘要：We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where band...
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作者：Chi, Zhiyi
作者单位：University of Connecticut
摘要：Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix c > 0 and p > 0. Let A(n) be the adjacency matrix of a random graph following G(n, p/n), known as the Erdos-Renyi distribution. Add c/n to each entry of A(n) and then normalize its rows. It is shown that the resulting Markov matrix has the desired properties. Its ESD weakly converges in probability to a symm...
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作者：Athreya, Siva; Rollin, Adrian
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; National University of Singapore
摘要：We consider certain respondent-driven sampling procedures on dense graphs. We show that if the sequence of the vertex-sets is ergodic then the limiting graph can be expressed in terms of the original dense graph via a transformation related to the invariant measure of the ergodic sequence. For specific sampling procedures, we describe the transformation explicitly.
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作者：Deijfen, Maria; van der Hofstad, Remco
作者单位：Stockholm University; Eindhoven University of Technology
摘要：We study competing first passage percolation on graphs generated by the configuration model. At time 0, vertex 1 and vertex 2 are infected with the type 1 and the type 2 infection, respectively, and an uninfected vertex then becomes type 1 (2) infected at rate lambda(1) (lambda(2)) times the number of edges connecting it to a type 1 (2) infected neighbor. Our main result is that, if the degree distribution is a power-law with exponent tau is an element of (2, 3), then as the number of vertices...
