Some sufficient conditions for Novikov’s criterion

Dung, Nguyen

doi:10.1090/proc/14074

Some sufficient conditions for Novikov’s criterion
HTML articles powered by AMS MathViewer

by Nguyen Tien Dung PDF

Proc. Amer. Math. Soc. 146 (2018), 3583-3590 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.