Stochastic Differential Equations and Diffusions in a Nutshell

  • Christiane Fuchs
Chapter

Abstract

Stochastic differential equations (SDEs) are a powerful and natural tool for the modelling of complex systems that change continuously in time. This chapter provides a short introduction to SDEs and their solutions, which under regularity conditions agree with the class of diffusion processes. In particular, it covers the motivation and introduction of stochastic integrals as opposed to the classical Lebesgue-Stieltjes integral, the definition of diffusion processes, key properties and formulas from stochastic calculus, and finally numerical approximation and exact sampling methods. The chapter serves as a basis for the remaining parts of this book and offers a quick access to stochastic calculus.

Keywords

Brownian Motion Stochastic Differential Equation Sample Path Transition Density Standard Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christiane Fuchs
    • 1
  1. 1.Institute for Bioinformatics and Systems BiologyHelmholtz Zentrum MünchenNeuherbergGermany

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