-
作者：Gnewuch, Michael; Hebbinghaus, Nils
作者单位：University Osnabruck; University of Kiel
摘要：We introduce a class of gamma-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a gamma-negatively dependent N-point sample in dimension d we provide probabilistic upper bounds for its star discrepancy with explicitly stated dependence on N, d, and gamma. These bounds generalize the probabilistic bounds for Monte Carlo samples from Heinrich et al. (...
-
作者：Diaconis, Persi; Houston-Edwards, Kelsey; Saloff-Coste, Laurent
作者单位：Stanford University; Franklin W. Olin College of Engineering; Cornell University
摘要：Gambler's ruin estimates can be viewed as harmonic measure estimates for finite Markov chains which are absorbed (or killed) at boundary points. We relate such estimates to properties of the underlying chain and its Doob transform. Precisely, we show that gambler's ruin estimates reduce to a good understanding of the Perron-Frobenius eigenfunction and eigenvalue whenever the underlying chain and its Doob transform are Harnack Markov chains. Finite inner-uniform domains (say, in the square grid...
-
作者：Ball, Frank
作者单位：University of Nottingham
摘要：We consider a stochastic SIR (susceptible -> infective -> recovered) epidemic defined on a configuration model random graph, in which infective individuals can infect only their neighbours in the graph during an infectious period which has an arbitrary but specified distribution. Central limit theorems for the final size (number of initial susceptibles that become infected) of such an epidemic as the population size n tends to infinity, with explicit, easy to compute expressions for the asympt...
-
作者：Gan, Han L.; Ross, Nathan
作者单位：Northwestern University; University of Melbourne
摘要：We provide a general theorem bounding the error in the approximation of a random measure of interest-for example, the empirical population measure of types in a Wright-Fisher model-and a Dirichlet process, which is a measure having Poisson-Dirichlet distributed atoms with i.i.d. labels from a diffuse distribution. The implicit metric of the approximation theorem captures the sizes and locations of the masses, and so also yields bounds on the approximation between the masses of the measure of i...
-
作者：Sun, Jingrui; Xiong, Jie; Yong, Jiongmin
作者单位：Southern University of Science & Technology; State University System of Florida; University of Central Florida
摘要：This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are allowed to be random and indefinite. It is shown, with a Hilbert space approach, that for the existence of an open-loop optimal control, the convexity of the cost functional (with respect to the control) is necessary; and the uniform convexity, which is slightly s...
-
作者：Henning, Florian; Kulske, Christof
作者单位：Ruhr University Bochum
摘要：We study gradient models for spins taking values in the integers (or an integer lattice), which interact via a general potential depending only on the differences of the spin values at neighboring sites, located on a regular tree with d + 1 neighbors. We first provide general conditions in terms of the relevant p-norms of the associated transfer operator Q which ensure the existence of a countable family of proper Gibbs measures, describing localization at different heights. Next we prove exis...
-
作者：Mangoubi, Oren; Smith, Aaron
作者单位：Worcester Polytechnic Institute; University of Ottawa
摘要：We obtain several quantitative bounds on the mixing properties of an ideal Hamiltonian Monte Carlo (HMC) Markov chain for a strongly log-concave target distribution pi on R-d. Our main result says that the HMC Markov chain generates a sample with Wasserstein error epsilon in roughly O(kappa(2) log(1/epsilon)) steps, where the condition number kappa = M-2/m(2) is the ratio of the maximum M-2 and minimum m(2) eigenvalues of the Hessian of - log(pi). In particular, this mixing bound does not depe...
-
作者：Du, Qiming; Guyader, Arnaud
作者单位：Universite Paris Cite; Sorbonne Universite; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Sorbonne Universite
摘要：Sequential Monte Carlo (SMC) methods represent a classical set of techniques to simulate a sequence of probability measures through a simple selection/mutation mechanism. However, the associated selection functions and mutation kernels usually depend on tuning parameters that are of first importance for the efficiency of the algorithm. A standard way to address this problem is to apply adaptive sequential Monte Carlo (ASMC) methods, which consist in exploiting the information given by the hist...
-
作者：Tomasevic, Milica
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Recently, we proposed a new stochastic interpretation of the parabolic-parabolic Keller-Segel system without cut-off via a McKean-Vlasov stochastic process. The process was defined through an original type of interaction kernel which involved, in a singular way, all its past time marginal distributions. In the present paper, we study this McKean-Vlasov representation in the two-dimensional case. In this setting, there exists a possibility of a blow-up in finite time for the Keller-Segel system...
-
作者：Andrieu, Christophe; Durmus, Alain; Nusken, Nikolas; Roussel, Julien
作者单位：University of Bristol; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Imperial College London; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Inria
摘要：In this work, we establish L-2-exponential convergence for a broad class of piecewise deterministic Markov processes recently proposed in the context of Markov process Monte Carlo methods and covering in particular the randomized Hamiltonian Monte Carlo (Trans. Amer. Math. Soc. 367 (2015) 3807-3828; Ann. Appl. Probab. 27 (2017) 2159-2194), the zig-zag process (Ann. Statist. 47 (2019) 1288-1320) and the bouncy particle Sampler (Phys. Rev. E 85 (2012) 026703; J. Amer. Statist. Assoc. 113 (2018) ...
