Table of Contents
ISRN Probability and Statistics
Volume 2014 (2014), Article ID 982190, 7 pages
http://dx.doi.org/10.1155/2014/982190
Research Article

Yamada-Watanabe Theorem for Stochastic Evolution Equation Driven by Poisson Random Measure

School of Applied Mathematics, Beijing Normal University Zhuhai, Zhuhai, Guangdong 519085, China

Received 27 October 2013; Accepted 11 December 2013; Published 2 February 2014

Academic Editors: C. Proppe and J. Villarroel

Copyright © 2014 Huiyan Zhao. 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. T. Yamada and S. Watanabe, “On the uniqueness of solutions of stochastic differential equations,” Journal of Mathematics of Kyoto University, vol. 11, pp. 155–167, 1971. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. G. Kurtz, “The Yamada-Watanabe-Engelbert theorem for general stochastic equations and inequalities,” Electronic Journal of Probability, vol. 12, pp. 951–965, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. G. Kurtz, “Weak and strong solutions of general stochastic models,” http://arxiv.org/abs/1305.6747.
  4. H. J. Engelbert, “On the theorem of T. Yamada and S. Watanabe,” Stochastics and Stochastics Reports, vol. 36, no. 3-4, pp. 205–216, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. S. Cherny, “On the uniqueness in law and the pathwise uniqueness for stochastic differential equations,” Teoriya Veroyatnostei i ee Primeneniya, vol. 46, no. 3, pp. 483–497, 2001. View at Publisher · View at Google Scholar
  6. M. Ondreját, “Uniqueness for stochastic evolution equations in Banach spaces,” Dissertationes Mathematicae, vol. 426, pp. 1–63, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Röckner, B. Schmuland, and X. Zhang, “Yamada-Watanabe theorem for stochastic evolution equations in infinite dimensions,” Condensed Matter Physics, vol. 11, no. 2, pp. 247–259, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, vol. 24 of North-Holland Mathematical Library, North-Holland, Amsterdam, The Netherlands, 1981. View at MathSciNet
  9. C. Prévôt and M. Röckner, A Concise Course on Stochastic Partial Differential Equations, vol. 1905 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. Budhiraja, J. Chen, and P. Dupuis, “Large deviations for stochastic partial differential equations driven by a Poisson random measure,” Stochastic Processes and their Applications, vol. 123, no. 2, pp. 523–560, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. N. V. Krylov and B. L. Rozovskii, “Stochastic evolution equations,” Itogi Naukii Tekhniki, Seriya Sovremennye Problemy Matematiki, vol. 14, pp. 71–146, 1979. View at Google Scholar
  12. S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise, vol. 113 of Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, UK, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Zhao, “On existence and uniqueness of stochastic evolution equation with Poisson jumps,” Statistics and Probability Letters, vol. 79, no. 22, pp. 2367–2373, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, vol. 288 of Grundlehren der Mathematischen Wissenschaften, Springer, Berlin, Germany, 1987. View at MathSciNet
  15. O. V. Pugachev, “The space of simple configuration is polish,” Mathematical Notes, vol. 71, no. 3-4, pp. 530–537, 2002, Translated from Matematicheskie Z ametki, vol. 71, no. 4 , pp. 581–589, 2002. View at Publisher · View at Google Scholar