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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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