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## Stochastic Simulation of Neurons, Axons, and Action Potentials

*A. Aldo Faisal*

### in Stochastic Methods in Neuroscience

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

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235070.003.0011
- Subject:
- Mathematics, Biostatistics

Variability is inherent in neurons. To account for variability we have to make use of stochastic models. We will take a look at this biologically more rigorous approach by studying the fundamental ... More

## Stochastic-Simulation Tests of Nonlinear Econometric Models

*Roberto S. Mariano and Bryan W. Brown*

### in Comparative Performance of U.S. Econometric Models

- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780195057720
- eISBN:
- 9780199854967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195057720.003.0009
- Subject:
- Economics and Finance, Econometrics

Stochastic simulations of nonlinear dynamic econometric models have been used in various ways in the past. This chapter discusses how stochastic simulations can be exploited to develop appropriate ... More

## Master equations and simulation algorithms for the discrete‐stochastic approach

*Daniel T. Gillespie and Effrosyni Seitaridou*

### in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664504
- eISBN:
- 9780191748516
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664504.003.0006
- Subject:
- Physics, Soft Matter / Biological Physics

The discrete-stochastic model of diffusion introduced in the preceding chapter implies that the system state evolves in time as what is known as a jump Markov process. The time evolution of such a ... More

## Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

*Daniel Thomas Gillespie and Effrosyni Seitaridou*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664504
- eISBN:
- 9780191748516
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664504.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics

Brownian diffusion is the motion of one or more solute molecules in a sea of very many, much smaller solvent molecules. Its importance today owes mainly to cellular chemistry, since Brownian ... More

## Numerical Simulation for Biochemical Kinetics

*Daniel T. Gillespie and Linda R. Petzold*

### in System Modeling in Cellular Biology: From Concepts to Nuts and Bolts

- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262195485
- eISBN:
- 9780262257060
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262195485.003.0016
- Subject:
- Mathematics, Mathematical Biology

This chapter discusses concepts and techniques for mathematically describing and numerically simulating chemical systems that into account discreteness and stochasticity. The chapter is organized as ... More

## Mathematical and computational modelling tools

*Baltazar D. Aguda and Avner Friedman*

### in Models of Cellular Regulation

- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198570912
- eISBN:
- 9780191718717
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570912.003.0003
- Subject:
- Physics, Soft Matter / Biological Physics

This chapter reviews chemical kinetics to illustrate the formulation of model equations for a given reaction mechanism. For spatially uniform systems, these model equations are usually ordinary ... More

## Notional Defined Contribution Pension Systems in a Stochastic Context: Design and Stability

*Ronald Lee*

*Alan J. Auerbach (ed.)*

### in Social Security Policy in a Changing Environment

- Published in print:
- 2009
- Published Online:
- February 2013
- ISBN:
- 9780226076485
- eISBN:
- 9780226076508
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226076508.003.0003
- Subject:
- Economics and Finance, Public and Welfare

This chapter explores a new approach to Social Security reform that is known as “Notional Defined Contribution” or “Nonfinancial Defined Contribution” (NDC). This chapter uses a stochastic ... More

## Computing Chemical Reactions

*Wolfgang Banzhaf and Lidia Yamamoto*

### in Artificial Chemistries

- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9780262029438
- eISBN:
- 9780262329460
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262029438.003.0004
- Subject:
- Public Health and Epidemiology, Public Health

This chapter examines various reactor algorithms that are frequently used in artificial chemistries. We contrast macroscopic, deterministic reaction algorithms and microscopic, stochastic reaction ... More

## Implications and limitations of the Einstein theory of diffusion

*Daniel T. Gillespie and Effrosyni Seitaridou*

### in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199664504
- eISBN:
- 9780191748516
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199664504.003.0004
- Subject:
- Physics, Soft Matter / Biological Physics

Chapter 3 showed how Einstein's analysis of Brownian motion shifted the focus of the classical diffusion equation from the average behavior of many solute molecules to the probabilistic behavior of ... More

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