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作者：Bresler, Guy; Nagaraj, Dheeraj
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov chains whose update rules are close in a certain sense. We apply this technique to compare Ising models on d-regular expander graphs to the Curie-Weiss model (complete graph) in terms of pairwise correlations and more generally kth order moments. Concretely, we show that d-regular Ramanujan graphs approximate the kth order moments of the Curie-Weiss model to within average erro...
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作者：Jacob, Emmanuel; Linker, Amitai; Moerters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; University of Cologne
摘要：We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomogeneous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For...
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作者：Marshall, Nicholas F.
作者单位：Yale University
摘要：Suppose f : [0, 1](2) -> R is a (c, alpha)-mixed Holder function that we sample at l points X-1,..., X-l chosen uniformly at random from the unit square. Let the location of these points and the function values f(X-1),..., f(X-l) be given. If l >= c(1)n log(2)n, then we can compute an approximation (f) over tilde such that parallel to integral -(integral) over tilde parallel to L-2 = O(n(-alpha) log(3/2)n), with probability at least 1- n(2-c1), where the implicit constant only depends on the c...
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作者：Cox, Alexander M. G.; Kinsley, Sam M.
作者单位：University of Bath
摘要：A leveraged exchange traded fund (LETF) is an exchange traded fund that uses financial derivatives to amplify the price changes of a basket of goods. In this paper, we consider the robust hedging of European options on a LETF, finding model-free bounds on the price of these options. To obtain an upper bound, we establish a new optimal solution to the Skorokhod embedding problem (SEP) using methods introduced in Beiglbock- Cox-Huesmann. This stopping time can be represented as the hitting time ...
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作者：Gu, Yu; Tsai, Li-Cheng
作者单位：Carnegie Mellon University; Columbia University
摘要：For the heat equation driven by a smooth, Gaussian random potential: partial derivative(t)u(epsilon) = 1/2 Delta u epsilon + u(epsilon) (xi(epsilon) - c(epsilon)), t > 0, chi is an element of R, where xi(e) converges to a spacetime white noise, and c(epsilon) is a diverging constant chosen properly, we prove that u(epsilon) converges in L-n to the solution of the stochastic heat equation for any n >= 1. Our proof is probabilistic, hence provides another perspective of the general result of Hai...
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作者：Hefter, Mario; Herzwurm, Andre; Mueller-Gronbach, Thomas
作者单位：Austrian Academy of Sciences; University of Kaiserslautern; University of Passau
摘要：We study pathwise approximation of scalar stochastic differential equations at a single time point or globally in time by means of methods that are based on finitely many observations of the driving Brownian motion. We prove lower error bounds in terms of the average number of evaluations of the driving Brownian motion that hold for every such method under rather mild assumptions on the coefficients of the equation. The underlying simple idea of our analysis is as follows: the lower error boun...
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作者：Viens, Frederi; Zhang, Jianfeng
作者单位：Michigan State University; University of Southern California
摘要：In this paper, we study dynamic backward problems, with the computation of conditional expectations as a special objective, in a framework where the (forward) state process satisfies a Volterra type SDE, with fractional Brownian motion as a typical example. Such processes are neither Markov processes nor semimartingales, and most notably, they feature a certain time inconsistency which makes any direct application of Markovian ideas, such as flow properties, impossible without passing to a pat...
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作者：Braunsteins, Peter; Hautphenne, Sophie
作者单位：University of Melbourne; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We consider a class of branching processes with countably many types which we refer to as Lower Hessenberg branching processes. These are multitype Galton-Watson processes with typeset X = {0, 1, 2,...}, in which individuals of type i may give birth to offspring of type j <= i + 1 only. For this class of processes, we study the set S of fixed points of the progeny generating function. In particular, we highlight the existence of a continuum of fixed points whose minimum is the global extinctio...
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作者：Huo, Ran; Durrett, Rick
作者单位：Duke University
摘要：Inspired by the spread of discontent as in the 2016 presidential election, we consider a voter model in which 0's are ordinary voters and 1's are zealots. Thinking of a social network, but desiring the simplicity of an infinite object that can have a nontrivial stationary distribution, space is represented by a tree. The dynamics are a variant of the biased voter: if x has degree d(x) then at rate d(x)p(k) the individual at x consults k >= 1 neighbors. If at least one neighbor is 1, they adopt...
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作者：Reinert, Gesine; Ross, Nathan
作者单位：University of Oxford; University of Melbourne
摘要：We provide a general bound on the Wasserstein distance between two arbitrary distributions of sequences of Bernoulli random variables. The bound is in terms of a mixing quantity for the Glauber dynamics of one of the sequences, and a simple expectation of the other. The result is applied to estimate, with explicit error, expectations of functions of random vectors for some Ising models and exponential random graphs in high temperature regimes.
