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Stochastic Differential Equations and Diffusions in a Nutshell

In: Inference for Diffusion Processes

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  • Christiane Fuchs

    (Helmholtz Zentrum München, Institute for Bioinformatics and Systems Biology)

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.

Suggested Citation

  • Christiane Fuchs, 2013. "Stochastic Differential Equations and Diffusions in a Nutshell," Springer Books, in: Inference for Diffusion Processes, edition 127, chapter 0, pages 31-53, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25969-2_3
    DOI: 10.1007/978-3-642-25969-2_3
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