-
作者：Craiu, Radu V.; Gray, Lawrence; Latuszynski, Krzysztof; Madras, Neal; Roberts, Gareth O.; Rosenthal, Jeffrey S.
作者单位：University of Toronto; University of Minnesota System; University of Minnesota Twin Cities; University of Warwick; York University - Canada
摘要：We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov chain Monte Carlo algorithms.
-
作者：Puha, Amber L.
作者单位：California State University System; California State University San Marcos
摘要：We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded support, it has been shown that standard diffusion scaling yields an identically zero limit. We specify an alternative spatial scaling that produces a nonzero limit. Our model allows for renewal arrivals and i.i.d. processing times satisfying a rapid variat...
-
作者：Bally, Vlad; Kohatsu-Higa, Arturo
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Inria; Ritsumeikan University; Japan Science & Technology Agency (JST)
摘要：In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is amenable to Monte Carlo simulation. We consider the explicit examples of continuous diffusions and jump driven stochastic differential equations with Holder continuous coefficients.
-
作者：Perl, Idan; Sen, Arnab; Yadin, Ariel
作者单位：Ben-Gurion University of the Negev; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study a model of growing population that competes for resources. At each time step, all existing particles reproduce and the offspring randomly move to neighboring sites. Then at any site with more than one offspring, the particles are annihilated. This is a nonmonotone model, which makes the analysis more difficult. We consider the extinction window of this model in the finite mean-field case, where there are n sites but movement is allowed to any site (the complete graph). We show that al...
-
作者：Lang, Annika; Schwab, Christoph
作者单位：Chalmers University of Technology; University of Gothenburg; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Loeve expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample Holder continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Loeve expansions in terms of the covariance spectrum are establishe...
-
作者：Pfaffelhuber, Peter; Popovic, Lea
作者单位：University of Freiburg; Concordia University - Canada
摘要：We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has differe...
-
作者：Le, Huiling
作者单位：University of Nottingham
摘要：This paper studies rescaled images, under exp(mu)(-1) of the sample Frechet means of i.i.d. random variables {X-k vertical bar k >= 1} with Frechet mean mu on a Riemannian manifold. We show that, with appropriate scaling, these images converge weakly to a diffusion process. Similar to the Euclidean case, this limiting diffusion is a Brownian motion up to a linear transformation. However, in addition to the covariance structure of exp(mu)(-1) (X-1), this linear transformation also depends on th...
