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Stochastic Differential Equations and Martingale Problems

  • Umut Çetin
  • Albina Danilova
Chapter
  • 452 Downloads
Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 90)

Abstract

In this chapter we explore the well posedness of martingale problems of Stroock and Varadhan. The results of this chapter will be crucial for solving the filtering equations of Chap.  3. This well posedness will be obtained by establishing the relationship between solutions of martingale problems and stochastic differential equations (SDEs). Thus, our focus in this chapter will be the connection between SDEs and martingale problems. To formulate the martingale problem we first need to develop the notion of an infinitesimal generator.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Umut Çetin
    • 1
  • Albina Danilova
    • 2
  1. 1.Department of StatisticsLondon School of EconomicsLondonUK
  2. 2.Department of MathematicsLondon School of EconomicsLondonUK

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