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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


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