Stochastic Differential Equations

  • Philip E. Protter
Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 21)


A diffusion can be thought of as a strong Markov process (in ℝ n ) 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.


Brownian Motion Stochastic Differential Equation Standard Brownian Motion Local Martingale Finite Variation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Philip E. Protter
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

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