Table of Contents
International Journal of Stochastic Analysis
Volume 2017, Article ID 2876961, 12 pages
https://doi.org/10.1155/2017/2876961
Research Article

Semigroup Solution of Path-Dependent Second-Order Parabolic Partial Differential Equations

Claremont Graduate University, Claremont, CA, USA

Correspondence should be addressed to Henry Schellhorn; ude.ugc@nrohllehcs.yrneh

Received 16 December 2016; Accepted 1 February 2017; Published 27 February 2017

Academic Editor: Lukasz Stettner

Copyright © 2017 Sixian Jin and Henry Schellhorn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Dupire, “Functional Ito calculus,” Portfolio Research Paper 2009-04, Bloomberg, 2009. View at Google Scholar
  2. R. Cont and D.-A. Fournie, “Functional Ito calculus and stochastic integral representation of martingales,” The Annals of Probability, vol. 41, no. 1, pp. 109–133, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. R. McOwen, Partial Differential Equations, Methods and Applications, Prentice Hall, 1996.
  4. K. Yosida, Functional Analysis, Springer, 1978. View at MathSciNet
  5. S. Jin, Q. Peng, and H. Schellhorn, “A representation theorem for smooth Brownian martingales,” Stochastics, vol. 88, no. 5, pp. 651–679, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. Peng and F. Wang, “BSDE, path-dependent PDE and nonlinear Feynman-Kac formula,” Science China Mathematics, vol. 59, no. 1, pp. 19–36, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. I. Ekren, C. Keller, N. Touzi, and J. Zhang, “On viscosity solutions of path dependent PDEs,” The Annals of Probability, vol. 42, no. 1, pp. 204–236, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. D. Nualart, The Malliavin Calculus and Related Topics, Springer, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, vol. 43 of Applications of Mathematics (New York), Springer, New York, NY, USA, 1999. View at Publisher · View at Google Scholar · View at MathSciNet