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Optimal filtration for systems with fractional Brownian noises
Author(s):
S.
V.
Posashkov
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 72
(2005).
Journal:
Theor. Probability and Math. Statist.
No. 72
(2006),
135-144.
MSC (2000):
Primary 60G35;
Secondary 60G15, 60H05, 60J65
Posted:
September 5, 2006
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Abstract:
We consider the problem of the optimal filtration for systems with the noise being a multivariate fractional Brownian motion. We partially solve the problem of the optimal filtration for nonlinear systems. The system of equations for the optimal filtration is obtained in the case of linear systems.
References:
-
- 1.
- R. Sh. Liptser and A. N. Shiryaev, Statistics of Random Processes, ``Nauka'', Moscow, 1974; English transl., Springer-Verlag, Berlin, 1977. MR 0431365 (55:4365)
- 2.
- G. Kallianpur, Stochastic Filtering Theory, Springer-Verlag, Berlin, 1980. MR 0583435 (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, 373-392.
- 4.
- -, General approach to filtering with fractional Brownian noises--application to linear systems, Stoch. Stoch. Rep. 71 (2000), 119-140. MR 1813509 (2001k:93131)
- 5.
- I. Norros, E. Valkeila, and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions, Bernoulli 5(4) (1999), 571-587. MR 1704556 (2000f:60053)
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Additional Information:
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
DOI:
10.1090/S0094-9000-06-00671-5
PII:
S 0094-9000(06)00671-5
Keywords:
Problem of filtration,
fractional Brownian motion
Received by editor(s):
2/JUL/2004
Posted:
September 5, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
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