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Random Processes in Physics and Finance

Melvin Lax, Wei Cai, and Min Xu

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567769
eISBN:
9780191718359
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567769.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book discusses random processes in physics, from basic probability theory to the Fokker-Planck process and Langevin equation for the Fokker Planck process and diffusion. It includes diverse ... 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


STOCHASTIC SET-BACKS

David Stirzaker

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0018
Subject:
Mathematics, Probability / Statistics

This chapter examines a random process (X(t):t ≥ 0) taking values in R, that is governed by the events of an independent renewal process N(t), as follows: whenever an event of N(t) occurs, the ... More


Analysis of Crossword Puzzle Difficulty Using a Random Graph Process

John K. McSweeney

in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.003.0008
Subject:
Mathematics, History of Mathematics

This chapter quantifies the dynamics of a crossword puzzle by using a network structure to model it. Specifically, the chapter determines how the interaction between the structure of cells in the ... More


STOCHASTIC PROCESSES

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter extends the ideas of Chapter 2 by introducing the notion of stochastic process or random process and its distribution functions. The idea of a Markov process is defined. The ... 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


Randomness

Peter Coles

in From Cosmos to Chaos: The Science of Unpredictability

Published in print:
2006
Published Online:
January 2010
ISBN:
9780198567622
eISBN:
9780191718250
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567622.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter examines randomness and how it applies (or does not) in both abstract mathematics and in physical systems. There are many different ways in which a sequence of events could be said to be ... 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


Non-Linear Cointegration in Foreign Exchange

Bernt P. Stigum

in Econometrics in a Formal Science of Economics: Theory and the Measurement of Economic Relations

Published in print:
2014
Published Online:
September 2015
ISBN:
9780262028585
eISBN:
9780262323109
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262028585.003.0008
Subject:
Economics and Finance, Econometrics

Chapter VIII presents a novel mathematical theory of non-linear cointegration among second-order random processes. It begins by explaining why the accepted characterization of integrated second-order ... More


Real-valued Random Processes

Arno Berger and Theodore P. Hill

in An Introduction to Benford's Law

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691163062
eISBN:
9781400866588
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691163062.003.0008
Subject:
Mathematics, Probability / Statistics

Benford's law arises naturally in a variety of stochastic settings, including products of independent random variables, mixtures of random samples from different distributions, and iterations of ... More


A Short Introduction to the Mathematical Theory of Benfordʼs Law

Arno Berger and T. P. Hill

in Benford's Law: Theory and Applications

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691147611
eISBN:
9781400866595
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147611.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter embarks on a brief discussion of the mathematical theory of Benford's law. This law is the observation that in many collections of numbers, be they mathematical tables, real-life data, ... More


Introduction to Probability

Therese M. Donovan and Ruth M. Mickey

in Bayesian Statistics for Beginners: a step-by-step approach

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198841296
eISBN:
9780191876820
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198841296.003.0001
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

In this chapter, the concept of probability is introduced. The rolling of a die is an example of a random process: the face that comes up is subject to chance. In probability, the goal is to quantify ... More


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