Optimal filtration in systems with noise modeled by a polynomial of fractional Brownian motion
Authors:
Yu. S. Mishura and S. V. Posashkov
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 73 (2006), 117-124
MSC (2000):
Primary 60G35; Secondary 60G15, 60H05, 60G65
DOI:
https://doi.org/10.1090/S0094-9000-07-00686-2
Published electronically:
January 17, 2007
MathSciNet review:
2213846
Full-text PDF Free Access
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Additional Information
Abstract: The problem of optimal filtration in systems with noise modeled by a polynomial of fractional Brownian motion is partially solved by representing fractional Brownian motion in terms of standard Brownian motion.
References
- R. S. Liptser and A. N. Shiryayev, Statistics of random processes. I, Springer-Verlag, New York-Heidelberg, 1977. General theory; Translated by A. B. Aries; Applications of Mathematics, Vol. 5. MR 0474486
- Gopinath Kallianpur, Stochastic filtering theory, Applications of Mathematics, vol. 13, Springer-Verlag, New York-Berlin, 1980. MR 583435
- M. L. Kleptsyna, A. Le Breton, and M. C. Roubaud, An elementary approach to filtering in systems with fractional Brownian observation noise, Probability Theory and Mathematical Statistics, Proceeding of the 7th Vilnius Conference, VSP/TEV, Utrecht/Vilnius, 2000, pp. 373–392.
- M. L. Kleptsyna, A. Le Breton, and M.-C. Roubaud, General approach to filtering with fractional Brownian noises—application to linear systems, Stochastics Stochastics Rep. 71 (2000), no. 1-2, 119–140. MR 1813509
- S. V. Posashkov, Optimal filtering in systems with fractional Brownian noise, Teor. Ĭmovīr. Mat. Stat. 72 (2005), 120–128 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 72 (2006), 135–144. MR 2168143, DOI https://doi.org/10.1090/S0094-9000-06-00671-5
- Ilkka Norros, Esko Valkeila, and Jorma Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli 5 (1999), no. 4, 571–587. MR 1704556, DOI https://doi.org/10.2307/3318691
References
- R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes. I. General Theory, “Nauka”, Moscow, 1974; English transl., Springer-Verlag, New York–Heidelberg, 1977. MR 0474486 (57:14125)
- G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, New York–Berlin, 1980. MR 583435 (82f:60089)
- M. L. Kleptsyna, A. Le Breton, and M. C. Roubaud, An elementary approach to filtering in systems with fractional Brownian observation noise, Probability Theory and Mathematical Statistics, Proceeding of the 7th Vilnius Conference, VSP/TEV, Utrecht/Vilnius, 2000, pp. 373–392.
- M. L. Kleptsyna, A. Le Breton, and M. C. Roubaud, General approach to filtering with fractional Brownian noises—application to linear systems, Stoch. Stoch. Rep. 71 (2000), 119–140. MR 1813509 (2001k:93131)
- S. V. Posashkov, Optimal filtration for systems with fractional Brownian noises, Teor. Ĭmovīr. Mat. Stat. 72 (2005), 120–128; English transl. in Theor. Probability and Math. Statist. 72 (2006), 135–144. MR 2168143 (2006f:60043)
- I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motion, Bernoulli 5(4) (1999), 571–587. MR 1704556 (2000f:60053)
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Additional Information
Yu. S. Mishura
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
myus@univ.kiev.ua
S. V. Posashkov
Affiliation:
Department of Probability Theory and Mathematical Statistics, Faculty for Mathematics and Mechanics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email:
corlagon@mail.univ.kiev.au
Keywords:
Problem of filtration,
fractional Brownian motion
Received by editor(s):
October 4, 2004
Published electronically:
January 17, 2007
Additional Notes:
The first author is supported in part by the grant NATO PST.CLG 890408
Article copyright:
© Copyright 2007
American Mathematical Society
