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

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **73** (2005).

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

Full-text PDF

Abstract | References | Similar Articles | 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.

**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. Imovr. 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)**

Retrieve articles in *Theory of Probability and Mathematical Statistics*
with MSC (2000):
60G35,
60G15,
60H05,
60G65

Retrieve articles in all journals with MSC (2000): 60G35, 60G15, 60H05, 60G65

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:
https://doi.org/10.1090/S0094-9000-07-00686-2

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