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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


The Mathematics of the Martingale Approach

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2004
Published Online:
October 2005
ISBN:
9780199271269
eISBN:
9780191602849
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199271267.003.0011
Subject:
Economics and Finance, Financial Economics

This chapter presents the two main workhorses of the martingale approach to arbitrage theory: the Martingale Representation Theorem and the Girsanov Theorem. The Martingale Representation Theorem ... More


Introduction and Overview

Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry

in Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198288107
eISBN:
9780191595899
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198288107.003.0001
Subject:
Economics and Finance, Econometrics

Serves as an introductory overview for the rest of the book, and outlines its main aims. As a basis for the following chapters, an overview and clarification of equilibrium relationships in economic ... More


Markov processes in continuous time and space

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/9780199575312.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Biology

Having dealt with processes in discrete space, and discrete and continuous time, this chapter investigates Markov processes in continuous space and time. It follows a natural progression through the ... More


Testing for a Unit Root

Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry

in Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198288107
eISBN:
9780191595899
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198288107.003.0004
Subject:
Economics and Finance, Econometrics

Methods of testing for a unit root in an observed series are described in this chapter. Both parametric regression tests and non‐parametric adjustments to these test statistics are considered, and ... More


Models in Finance

GREGORY C. CHOW

in Dynamic Economics: Optimization by the Lagrange Method

Published in print:
1997
Published Online:
October 2011
ISBN:
9780195101928
eISBN:
9780199855032
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195101928.003.0007
Subject:
Economics and Finance, Financial Economics

Using stochastic differential equations instead of utilizing stochastic difference equations, most of the models involved in finance follow Merton’s work and are developed in continuous time. In this ... More


Stochastic Integrals

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2019
Published Online:
February 2020
ISBN:
9780198851615
eISBN:
9780191886218
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851615.003.0004
Subject:
Economics and Finance, Econometrics

We introduce the Wiener process, the Itô stochastic integral, and derive the Itô formula. The connection with martingale theory is discussed, and there are several worked-out examples


Large Deviations Principle for Diffusions

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/9780199657063.003.0012
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

Large deviations theory formulated by Varadhan has made a tremendous impact in a variety of fields such as mathematical physics, control theory, and statistics, to name a few. After a brief ... More


Distributions of High-Frequency Stock-Market Observables

Roberto Osorio and Lisa Borland

in Nonextensive Entropy: Interdisciplinary Applications

Published in print:
2004
Published Online:
November 2020
ISBN:
9780195159769
eISBN:
9780197562024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195159769.003.0023
Subject:
Earth Sciences and Geography, Atmospheric Sciences

Power laws and scaling are two features that have been known for some time in the distribution of returns (i.e., price fluctuations), and, more recently, in the ... More


The Pricing of Stock Options

Lisa Borland

in Nonextensive Entropy: Interdisciplinary Applications

Published in print:
2004
Published Online:
November 2020
ISBN:
9780195159769
eISBN:
9780197562024
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195159769.003.0022
Subject:
Earth Sciences and Geography, Atmospheric Sciences

We describe how a stock price model based on nonextensive statistics can be used to derive a generalized theory for pricing stock options. A review of theoretical and ... More


Stochastic Equations Of Motion

Abraham Nitzan

in Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198529798
eISBN:
9780191916649
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198529798.003.0014
Subject:
Chemistry, Physical Chemistry

We have already observed that the full phase space description of a system of N particles (taking all 6N coordinates and velocities into account) requires ... More


Manifolds, Active Models, And Deformable Templates

Ulf Grenander and Michael I. Miller

in Pattern Theory: From representation to inference

Published in print:
2006
Published Online:
November 2020
ISBN:
9780198505709
eISBN:
9780191916564
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198505709.003.0009
Subject:
Computer Science, Programming Languages

To study shape we introduce manifolds and submanifolds examined in the continuum as the generators. Transformations are constructed which are built from the matrix ... More


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