Stochastic Differential Equations

  • Ioannis Karatzas
  • Steven E. Shreve
Part of the Graduate Texts in Mathematics book series (GTM, volume 113)


We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.


Weak Solution Stochastic Differential Equation Strong Solution Contingent Claim Local Martingale 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Ioannis Karatzas
    • 1
  • Steven E. Shreve
    • 2
  1. 1.Departments of Mathematics and StatisticsColumbia UniversityNew YorkUSA
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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