Some sufficient conditions for Novikov’s criterion
HTML articles powered by AMS MathViewer
- by Nguyen Tien Dung
- Proc. Amer. Math. Soc. 146 (2018), 3583-3590
- DOI: https://doi.org/10.1090/proc/14074
- Published electronically: May 2, 2018
- PDF | Request permission
Abstract:
In this note, we employ the techniques of Malliavin calculus to provide some sufficient conditions for a stochastic process to satisfy Novikov’s criterion. In particular, we obtain an improvement for Buckdahn’s results established in Probab. Theory Related Fields 89 (1991), 211-238 and a generalization of Borell-TIS inequality.References
- Robert J. Adler and Jonathan E. Taylor, Random fields and geometry, Springer Monographs in Mathematics, Springer, New York, 2007. MR 2319516
- Rainer Buckdahn, Anticipative Girsanov transformations, Probab. Theory Related Fields 89 (1991), no. 2, 211–238. MR 1110539, DOI 10.1007/BF01366907
- Ognian Enchev, Nonlinear transformations on the Wiener space, Ann. Probab. 21 (1993), no. 4, 2169–2188. MR 1245305
- Pavel V. Gapeev and Neofytos Rodosthenous, Optimal stopping problems in diffusion-type models with running maxima and drawdowns, J. Appl. Probab. 51 (2014), no. 3, 799–817. MR 3256228, DOI 10.1239/jap/1409932675
- Monique Jeanblanc, Marc Yor, and Marc Chesney, Mathematical methods for financial markets, Springer Finance, Springer-Verlag London, Ltd., London, 2009. MR 2568861, DOI 10.1007/978-1-84628-737-4
- Ioannis Karatzas and Steven E. Shreve, Brownian motion and stochastic calculus, 2nd ed., Graduate Texts in Mathematics, vol. 113, Springer-Verlag, New York, 1991. MR 1121940, DOI 10.1007/978-1-4612-0949-2
- A. A. Novikov, On moment inequalities and identities for stochastic integrals, Proceedings of the Second Japan-USSR Symposium on Probability Theory (Kyoto, 1972) Lecture Notes in Math., Vol. 330, Springer, Berlin, 1973, pp. 333–339. MR 0448553
- Bernt Øksendal, Stochastic differential equations, 6th ed., Universitext, Springer-Verlag, Berlin, 2003. An introduction with applications. MR 2001996, DOI 10.1007/978-3-642-14394-6
- David Nualart, The Malliavin calculus and related topics, 2nd ed., Probability and its Applications (New York), Springer-Verlag, Berlin, 2006. MR 2200233
- Amir Dembo and Ofer Zeitouni, Large deviations techniques and applications, 2nd ed., Applications of Mathematics (New York), vol. 38, Springer-Verlag, New York, 1998. MR 1619036, DOI 10.1007/978-1-4612-5320-4
- A.S. Üstünel, 2015. Analysis on Wiener Space and Applications. arXiv:1003.1649v2.
Bibliographic Information
- Nguyen Tien Dung
- Affiliation: Department of Mathematics, FPT University, Hoa Lac High Tech Park, Hanoi, Vietnam
- MR Author ID: 859302
- Email: dung_nguyentien10@yahoo.com, dungnt@fpt.edu.vn
- Received by editor(s): August 31, 2016
- Received by editor(s) in revised form: July 20, 2017
- Published electronically: May 2, 2018
- Additional Notes: This research was funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2015.15.
- Communicated by: David Levin
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3583-3590
- MSC (2010): Primary 60G07, 60H07
- DOI: https://doi.org/10.1090/proc/14074
- MathSciNet review: 3803682