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Power-Law Dynamic Arising from Machine Learning
We study a kind of new SDE that was arisen from the research on optimization in machine learning, we call it power-law dynamic because its stationary...
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Doob Decomposition, Dirichlet Processes, and Entropies on Wiener Space
As an extension of the Doob-Meyer decomposition of a semimartingale and the Fukushima representation of a Dirichlet process, we introduce a general...
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On \(L^p\) Liouville Theorems for Dirichlet Forms
We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima’s ergodic theorem for the harmonic functions in...
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Singularity of Energy Measures on a Class of Inhomogeneous Sierpinski Gaskets
We study energy measures of canonical Dirichlet forms on inhomogeneous Sierpinski gaskets. We prove that the energy measures and suitable reference...
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Bayesian Nonparametric Predictive Modeling for Personalized Treatment Selection
Pedone, Matteo Argiento, Raffaele Stingo, C.We develop a Bayesian nonparametric predictive model to establish personalized therapeutic strategies for...
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Specification of the Base Measure of Nonparametric Priors via Random Means
Gaffi, Francesco Lijoi, Antonio Prünster, IgorFunctionals of random probability measures are probabilistic objects whose properties are studied in...
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Power-Expected-Posterior Methodology with Baseline Shrinkage Priors
Tzoumerkas, G. Fouskakis, D.The Power-Expected-Posterior (PEP) prior gives us a convenient and objective method to deal with variable selection...
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A Bayesian Joint Spatio-temporal Model for Multiple Mosquito-Borne Diseases
Pavani, Jessica Moraga, PaulaMany infectious diseases studied in the epidemiological context are caused by insects, mainly mosquitoes. These...
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Bayesian Growth Curve Model for Studying the Intra-abdominal Volume During Pneumoperitoneum for Laparoscopic Surgery
Calvo, Gabriel Armero, Carmen Gómez-Rubio, Virgilio Mazzinari, GuidoLaparoscopy is a surgical procedure carried out in the abdomen or pelvis through...
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Bayesian Quantile Regression for Big Data Analysis
Chu, Yuanqi Hu, Xue** Yu, KemingQuantile regression, which estimates various conditional quantiles of a response variable, including the median...
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Block Structured Graph Priors in Gaussian Graphical Models
Colombi, AlessandroGaussian graphical models are a powerful statistical tool to describe the concept of conditional independence between variables...
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Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results
This article gives an overview of some recent progress in the study of sharp two-sided estimates for the transition density of a large class of...
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Equivalence of the Strong Feller Properties of Analytic Semigroups and Associated Resolvents
In this paper, we give sufficient conditions for the equivalence between semigroup strong Feller property and resolvent strong Feller property.
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Maximal Displacement of Branching Symmetric Stable Processes
We determine the limiting distribution and the explicit tail behavior for the maximal displacement of a branching symmetric stable process with...
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On Non-negative Solutions to Space-Time Partial Differential Equations of Higher Order
We discuss when certain higher order partial differential operators in space and time admit non-negative solutions which have a semigroup...
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Dyson’s Model in Infinite Dimensions Is Irreducible
Dyson’s model in infinite dimensions is a system of Brownian particles interacting via a logarithmic potential with an inverse temperature of...
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Scattering Lengths for Additive Functionals and Their Semi-classical Asymptotics
Scattering lengths for positive additive functionals of symmetric Markov processes are studied. The additive functionals considered here are not...
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Interactions Between Trees and Loops, and Their Representation in Fock Space
It has been observed that on a weighted graph, an extension of Wilson’s algorithm provides an independent pair...
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Hölder Estimates for Resolvents of Time-Changed Brownian Motions
In this paper, we study time changes of Brownian motions by positive continuous additive functionals. Under a certain regularity condition on the...
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On Singularity of Energy Measures for Symmetric Diffusions with Full Off-Diagonal Heat Kernel Estimates II: Some Borderline Examples
We present a concrete family of fractals, which we call the (two-dimensional) thin scale irregular Sierpiński gaskets and each of which is equipped...