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INTRODUCTION

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0001
Subject:
Mathematics, Probability / Statistics

This introductory chapter contains a general discussion of both the historical and the applied background behind the study of random geometric graphs. A brief overview is presented, along with some ... More


PERCOLATIVE INGREDIENTS

Mathew Penrose

in Random Geometric Graphs

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506263
eISBN:
9780191707858
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506263.003.0009
Subject:
Mathematics, Probability / Statistics

This chapter contains some known results on connectivity which are used later on. The notion of unicoherence of a simply-connected set is explained and extended to lattices. Peierls (counting) ... More


Simple Markov population processes

Eric Renshaw

in Stochastic Population Processes: Analysis, Approximations, Simulations

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199575312
eISBN:
9780191728778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575312.003.0002
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

This chapter explains the basic principles which underlie the concept of stochastic population dynamics by considering some simple types of population structure. Suppose that individuals develop ... More


Population Density Methods in Large-Scale Neural Network Modelling

Daniel Tranchina

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0007
Subject:
Mathematics, Biostatistics

Population density methods have a rich history in theoretical and computational neuroscience. In earlier years, these methods were used in large part to study the statistics of spike trains. Starting ... More


Jump Markov Processes

Gopinath Kallianpur and P. Sundar

in Stochastic Analysis and Diffusion Processes

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.003.0010
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

After introducing Poisson processes, the form of their generators is explained. Jump Markov processes, generators, and explosion times are discussed. Skorohod space is introduced, and the proof of ... More


Default Correlation

Darrell Duffie

in Measuring Corporate Default Risk

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199279234
eISBN:
9780191728419
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199279234.003.0005
Subject:
Economics and Finance, Financial Economics

This chapter provides a battery of tests of the ability of the model estimated in Chapter 4 to capture default correlation. Several of these tests are based on a time re-scaling by which defaults ... More


Simulating molecular evolution

Ziheng Yang

in Molecular Evolution: A Statistical Approach

Published in print:
2014
Published Online:
August 2014
ISBN:
9780199602605
eISBN:
9780191782251
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199602605.003.0012
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Evolutionary Biology / Genetics

This chapter introduces computer simulation and in particular simulation of the molecular evolutionary process. It covers the generation of random numbers as well as other discrete and continuous ... More


Introduction to replica theory

Marc Mézard and Andrea Montanari

in Information, Physics, and Computation

Published in print:
2009
Published Online:
September 2009
ISBN:
9780198570837
eISBN:
9780191718755
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570837.003.0008
Subject:
Physics, Theoretical, Computational, and Statistical Physics

In the past twenty-five years, the replica method has evolved into a rather sophisticated tool for attacking theoretical problems as diverse as spin glasses, protein folding, vortices in ... More


Rotating Stars and Revolving Planets: Bayesian Exploration of the Pulsating Sky *

Thomas J. Loredo

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0012
Subject:
Mathematics, Probability / Statistics

I describe ongoing work on the development of Bayesian methods for exploring periodically varying phenomena in astronomy, addressing two classes of sources: pulsars, and extrasolar planets ... More


Examples of Markovian processes

Melvin Lax, Wei Cai, and Min Xu

in Random Processes in Physics and Finance

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Consider two physical problems describable by the same random process. The first process is the radioactive decay of a collection of nuclei. The second is the production of photoelectrons by a steady ... More


Continuous-Time Topics

Kerry E. Back

in Asset Pricing and Portfolio Choice Theory

Published in print:
2017
Published Online:
May 2017
ISBN:
9780190241148
eISBN:
9780190241179
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780190241148.003.0015
Subject:
Economics and Finance, Financial Economics

The fundamental PDE for valuing cash flows or cash flow streams is explained. In a complete market, an investor’s optimal wealth satisfies the fundamental PDE, and this provides a means of ... More


Inference for models with asymmetric α -stable noise processes

Tatjana Lemke and Simon J. Godsill

in Unobserved Components and Time Series Econometrics

Published in print:
2015
Published Online:
January 2016
ISBN:
9780199683666
eISBN:
9780191763298
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199683666.003.0009
Subject:
Economics and Finance, Econometrics

This chapter begins with a simple general framework for inference in the presence of α‎-stable processes, where the stable processes are represented as conditionally Gaussian distributions, relying ... More


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