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Stochastic Functional (Partial) Differential Equations

  • Feng-Yu Wang
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we investigate Harnack/shift Harnack inequalities and derivative formulas for stochastic functional differential equations. In this case, the strong or mild solution is no longer Markovian. These inequalities and formulas are therefore established for the semigroup associated with the functional (or segment) solutions. To this end, a time larger than the length of delay is necessary in order to construct a successful coupling by change of measure. Based on Bao et al. (Derivative formula and Harnack inequality for degenerate functional SDEs, to appear in Stochast. Dynam.; Bismut Formulae and Applications for Functional SPDEs, to appear in Bull. Math. Sci.), Shao et al. (Electron. J. Probab. 17:1–18, 2012), Wang and Yuan (Stoch. Process. Their Appl. 121:2692–2710, 2011), several specific models of elliptic SDDEs, semilinear SDPDEs, and degenerate SDDEs are considered.

Keywords

Brownian Motion Mild Solution Harnack Inequality Coupling Time Malliavin Calculus 
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.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Feng-Yu Wang
    • 1
    • 2
  1. 1.School of Mathematical SciencesBeijing Normal UniversityBeijingChina, People’s Republic
  2. 2.Department of MathematicsSwansea UniversitySwanseaUK

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