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Stochastic differential equations

  • Dmytro Gusak
  • Alexander Kukush
  • Alexey Kulik
  • Yuliya Mishura
  • Andrey Pilipenko
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Consider a complete filtration \({\mathcal{F}}_t\), t∈[0,T]} and an m-dimensional Wiener process {W(t), t ∈ [0,T]} with respect to it. By definition, a stochastic differential equation (SDE) is an equation of the form with X 0=ξ, where ξ is an \({\mathcal{F}}_0\)-measurable random vector, \(b=b(t,x): [0,T]\times \mathbb{R}^n\rightarrow \mathbb{R}^n\), and \(\sigma=\sigma(t,x): [0,T]\times \mathbb{R}^n\rightarrow \mathbb{R}^{n\times m}\) are measurable functions.

Keywords

Stochastic Differential Equation Wiener Process Exit Time Brownian Bridge Uhlenbeck Process 
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.

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Dmytro Gusak
    • 1
  • Alexander Kukush
    • 2
  • Alexey Kulik
    • 1
  • Yuliya Mishura
    • 3
  • Andrey Pilipenko
    • 1
  1. 1.Institute of Mathematics of Ukrainian National Academy of SciencesKyivUkraine
  2. 2.Department of Mathematical Analysis Faculty of Mechanics and MathematicsNational Taras Shevchenko University of KyivKyivUkraine
  3. 3.Department of Probability Theory and Mathematical Statistics Faculty of Mechanics and MathematicsNational Taras Shevchencko University of KyivKyivUkraine

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