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Optimal filtration in systems with noise modeled by a polynomial of fractional Brownian motion
Author(s):
Yu.
S.
Mishura;
S.
V.
Posashkov
Translated by:
Oleg Klesov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 73
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 73
(2006),
117-124.
MSC (2000):
Primary 60G35;
Secondary 60G15, 60H05, 60G65
Posted:
January 17, 2007
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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:
-
- 1.
- 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)
- 2.
- G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, New York-Berlin, 1980. MR 583435 (82f:60089)
- 3.
- 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.
- 4.
- 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)
- 5.
- S. V. Posashkov, Optimal filtration for systems with fractional Brownian noises, Teor. Imov
 r. Mat. Stat. 72 (2005), 120-128; English transl. in Theor. Probability and Math. Statist. 72 (2006), 135-144. MR 2168143 (2006f:60043) - 6.
- 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
DOI:
10.1090/S0094-9000-07-00686-2
PII:
S 0094-9000(07)00686-2
Keywords:
Problem of filtration,
fractional Brownian motion
Received by editor(s):
4/OCT/2004
Posted:
January 17, 2007
Additional Notes:
The first author is supported in part by the grant NATO PST.CLG 890408
Copyright of article:
Copyright
2007,
American Mathematical Society
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