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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

## 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 empirical results is ... 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 the solution of the deterministic Newton ... More

## Distributions of High-Frequency Stock Market Observables

*Roberto Osorio, Lisa Borland, and Constantino Tsallis*

### 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 distribution of volumes (i.e., ... 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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