Abstract
A diffusion can be thought of as a strong Markov process (in ℝn) with continuous paths. Before the development of Itô’s theory of stochastic integration for Brownian motion, the primary method of studying diffusions was to study their transition semigroups. This was equivalent to studying the infinitesimal generators of their semigroups, which are partial differential operators. Thus Feller’s investigations of diffusions (for example) were actually investigations of partial differential equations, inspired by diffusions.
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© 2005 Springer-Verlag Berlin Heidelberg
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Protter, P.E. (2005). Stochastic Differential Equations. In: Stochastic Integration and Differential Equations. Stochastic Modelling and Applied Probability, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10061-5_6
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DOI: https://doi.org/10.1007/978-3-662-10061-5_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05560-7
Online ISBN: 978-3-662-10061-5
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