# Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition

@inproceedings{Gardiner1985HandbookOS, title={Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition}, author={Crispin W. Gardiner}, booktitle={Springer series in synergetics}, year={1985} }

The Handbook of Stochastic Methods covers systematically and in simple language the foundations of Markov systems, stochastic differential equations, Fokker-Planck equations, approximation methods, chemical master equations, and quatum-mechanical Markov processes. Strong emphasis is placed on systematic approximation methods for solving problems. Stochastic adiabatic elimination is newly formulated. The book contains the "folklore" of stochastic methods in systematic form and is suitable for…

## 2,423 Citations

A Langevin approach to the macroscopic stochasticity of chemical systems

- Mathematics
- 1988

A theoretical approach to the problem of the marked irreproducibility of certain chemical reactions studied by Epstein’s group at Brandeis University is presented. The model is based on the use of a…

Modeling and Simulating Chemical Reactions

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- 2008

Some of the basic concepts of deterministic reaction rate equations are introduced in an accessible manner and some challenges that currently occupy researchers in this area are pointed to.

Integration of Langevin equations with multiplicative noise and the viability of field theories for absorbing phase transitions.

- PhysicsPhysical review letters
- 2005

The computational power of the split-step scheme is demonstrated by applying it to the most absorbing phase transitions for which Langevin equations have been proposed, providing precise estimates of the associated scaling exponents, clarifying the classification of these nonequilibrium problems, and confirms or refutes some existing theories.

Numerical Methods for Stochastic Simulation: When Stochastic Integration Meets Geometric Numerical Integration

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- 2017

It is described how ideas originating from geometric numerical integration or structure preserving methods for deterministic differential equations can help to design new integrators for weak approximation of stochastic differential equations or for long-time simulation of ergodic Stochastic systems.

Appendix: The Master Equation

- Physics
- 1989

The master equation provides a fairly general mathematical method for describing the time development of any complex system (see Weidlich and Haag1). Before going into details of its structure, some…

Application of stochastic point processes in mechanics

- Chemistry, Mathematics
- 2009

Stochastic point processes are the mathematical tools relevant to all problems where the phenomena have the nature of a random train of events. Applications may be found in structural dynamics where…

Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics

- Computer Science
- 2002

This paper addresses one aspect of this problem: the case in which reacting species fluctuate by different orders of magnitude, and provides a theoretical background for such approximations and outlines strategies for computing these approximation.

Stochastic Kinetics: Why and How?

- Physics
- 2014

Chemical kinetics is a prototype of nonlinear science. Traditionally, chemical systems can be characterized by the concentrations of the species, and the temporal evolution is governed by (generally…