## System Control and Rough Paths

*Terry Lyons and Zhongmin Qian*

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.001.0001
- Subject:
- Mathematics, Probability / Statistics

Systems evolve and interact, and when they do this in a continuous way, differential equations can be used to provide accurate mathematical models for the interaction or reaction of the controlled ... More

## Numerical Methods for Structured Markov Chains

*Dario A. Bini, Guy Latouche, and Beatrice Meini*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198527688
- eISBN:
- 9780191713286
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527688.001.0001
- Subject:
- Mathematics, Numerical Analysis

The book deals with the numerical solution of structured Markov chains which include M/G/1 and G/M/1-type Markov chains, QBD processes, non-skip-free queues, and tree-like stochastic processes and ... More

## Random Geometric Graphs

*Mathew Penrose*

- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.001.0001
- Subject:
- Mathematics, Probability / Statistics

This book sets out a body of rigorous mathematical theory for finite graphs with nodes placed randomly in Euclidean d-space according to a common probability density, and edges added to connect ... More

## Stochastic Methods in Neuroscience

*Carlo Laing and Gabriel J Lord (eds)*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199235070
- eISBN:
- 9780191715778
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235070.001.0001
- Subject:
- Mathematics, Biostatistics

We give a brief introduction to modelling in mathematical neuroscience, to stochastic processes, and stochastic differential equations as well as an overview of the book.

## New Perspectives in Stochastic Geometry

*Wilfrid S. Kendall and Ilya Molchanov (eds)*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199232574
- eISBN:
- 9780191716393
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232574.001.0001
- Subject:
- Mathematics, Geometry / Topology

Stochastic geometry is a subject with roots stretching back at least 300 years, but one which has only been formed as an academic area in the last 50 years. It covers the study of random patterns, ... More

## Computational Methods for the Study of Dynamic Economies

*Ramon Marimon and Andrew Scott (eds)*

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics

Macroeconomics increasingly uses stochastic dynamic general equilibrium models to understand theoretical and policy issues. Unless very strong assumptions are made, understanding the properties of ... More

## Stochastic Modeling and Analysis

*Richard M. Murray*

### in Biomolecular Feedback Systems

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.003.0004
- Subject:
- Biology, Biochemistry / Molecular Biology

This chapter explores stochastic behavior in biomolecular systems. It does so by first building on the preliminary discussion of stochastic modeling laid out in Chapter 2. The chapter reviews methods ... More

## Introduction

*Anthony Garratt, Kevin Lee, M. Hashem Pesaran, and Yongcheol Shin*

### in Global and National Macroeconometric Modelling: A Long-Run Structural Approach

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199296859
- eISBN:
- 9780191603853
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199296855.003.0001
- Subject:
- Economics and Finance, Econometrics

This chapter introduces the long-run structural approach to modelling. It makes brief comparisons with the key alternative approaches, namely large-scale simultaneous equation models, unrestricted ... More

## Probability forecasting: Concepts and analysis

*Anthony Garratt, Kevin Lee, M. Hashem Pesaran, and Yongcheol Shin*

### in Global and National Macroeconometric Modelling: A Long-Run Structural Approach

- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780199296859
- eISBN:
- 9780191603853
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199296855.003.0007
- Subject:
- Economics and Finance, Econometrics

This chapter provides an introduction to the interpretation and estimation of probability forecasts, which is considered to be a particularly useful method for presenting forecasts and ... More

## Country default risk in emerging markets 1

*Jerome L. Stein*

### in Stochastic Optimal Control, International Finance, and Debt Crises

- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199280575
- eISBN:
- 9780191603501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280576.003.0007
- Subject:
- Economics and Finance, Financial Economics

Early Warning Signals of a default or debt crisis are derived by drawing upon the stochastic optimal control model of an optimal and excessive short-term debt developed in chapter 2. Operational ... More

## Asian crises: Theory, evidence, warning Signals 1

*Jerome L. Stein*

### in Stochastic Optimal Control, International Finance, and Debt Crises

- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199280575
- eISBN:
- 9780191603501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280576.003.0008
- Subject:
- Economics and Finance, Financial Economics

The Asian financial crises were unexpected by the market and many countries in the region experienced it at about the same time. Drawing upon the theoretical analyses in chapters 2-4, an operational ... More

## United States current account deficits: A stochastic optimal control analysis 1

*Jerome L. Stein*

### in Stochastic Optimal Control, International Finance, and Debt Crises

- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199280575
- eISBN:
- 9780191603501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280576.003.0009
- Subject:
- Economics and Finance, Financial Economics

For nearly a quarter of a century, the US has persistently run significant current account deficits that transformed it from the world’s largest net creditor to its largest debtor. The stochastic ... More

## Biomolecular Feedback Systems

*Domitilla Del Vecchio and Richard M. Murray*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161532
- eISBN:
- 9781400850501
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161532.001.0001
- Subject:
- Biology, Biochemistry / Molecular Biology

This book provides an accessible introduction to the principles and tools for modeling, analyzing, and synthesizing biomolecular systems. It begins with modeling tools such as reaction-rate ... More

## On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics

*A.D. Neate and A. Truman*

### in Analysis and Stochastics of Growth Processes and Interface Models

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0013
- Subject:
- Mathematics, Probability / Statistics, Analysis

This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces ... More

## Optimal Fiscal Policy in a Linear Stochastic Economy

*Thomas J. Sargent and François R. Velde*

### in Computational Methods for the Study of Dynamic Economies

- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199248278
- eISBN:
- 9780191596605
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199248273.003.0009
- Subject:
- Economics and Finance, Macro- and Monetary Economics

The Lucas and Stokey (1983) economy without capital is used to exhibit features of the Lucas and Stokey model of optimal taxation, and show how they compare with Barro's (1979) tax‐smoothing model. ... More

## Brownian Motion: Fluctuations, Dynamics, and Applications

*Robert M. Mazo*

- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199556441
- eISBN:
- 9780191705625
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199556441.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

Brownian motion is the incessant motion of small particles immersed in an ambient medium. It is due to fluctuations in the motion of the medium particles on the molecular scale. The name has been ... More

## Survival Modeling

*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/9780199279234.003.0002
- Subject:
- Economics and Finance, Financial Economics

This chapter provides the mathematical foundations for stochastic intensity, on which most of the methodology is based. The intensity of an event such as default is its conditional mean arrival rate, ... More

## Stochastic Population Processes: Analysis, Approximations, Simulations

*Eric Renshaw*

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199575312
- eISBN:
- 9780191728778
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575312.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Biology

The vast majority of random processes in the real world have no memory — the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely ... More

## What is a random process

*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/9780198567769.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A random or stochastic process is a random variable that evolves in time by some random mechanism (of course, the time variable can be replaced by a space variable, or some other variable, in ... More

## Reforming the German Civil Servant Pension Plan

*Raimond Maurer, Olivia S. Mitchell, and Ralph Rogalla*

### in The Future of Public Employee Retirement Systems

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573349
- eISBN:
- 9780191721946
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573349.003.0009
- Subject:
- Business and Management, Public Management, Pensions and Pension Management

This chapter analyzes the risks and rewards of moving from an unfunded defined benefit pension system to a funded plan for civil servants in Germany, allowing for alternative portfolio mixes using a ... More