Geodesic
On the estimation of backward stochastic differential equations
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 17-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an estimation problem for a backward stochastic differential equation in the presence of statistically indeterminate noise. We use the approach of the theory of guaranteed estimation and assume that the statistically indeterminate noise, as well as some processes entering the equation, is subject to integral constraints. In the linear case, we prove a theorem on the approximation of random information sets by deterministic sets as the diffusion coefficient vanishes. Examples are considered.
Keywords: backward stochastic differential equation, Brownian motion, random information set. 
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B. I. Anan'ev. On the estimation of backward stochastic differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 4, pp. 17-28. http://geodesic.mathdoc.fr/item/TIMM_2014_20_4_a1/

[1] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 306 pp. | MR | Zbl

[2] Kurzhanskii A. B., “Printsip sravneniya dlya uravnenii tipa Gamiltona–Yakobi v teorii upravleniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 12, no. 1, 2006, 173–183 | MR | Zbl

[3] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, Nonsmooth analysis and control theory, Springer-Verlag, New York, 1998, 276 pp. | MR | Zbl

[4] Bulinskii A. V., Shiryaev A. N., Teoriya sluchainykh protsessov, Fizmatlit, M., 2003, 399 pp.

[5] Kallianpur G., Stokhasticheskaya teoriya filtratsii, Nauka, M., 1987, 318 pp. | MR | Zbl

[6] Yong J., Zhou X., Stochastic controls: Hamiltonian systems and HJB equations, Springer-Verlag, New York, 1999, 438 pp. | MR

[7] Bismut J. M., “An introductory approach to duality in optimal stochastic control”, SIAM Rev., 20 (1978), 62–78 | DOI | MR | Zbl

[8] Ananev B. I., “Otsenivanie sostoyanii obratnykh stokhasticheskikh differentsialnykh uravnenii so statisticheski neopredelennymi pomekhami”, XII Vserossiiskoe soveschanie po problemam upravleniya – VSPU-2014, Sb. dokl. (Moskva, 16–19 iyunya, 2014 g.), 2604–2611, [Elektron. resurs]

[9] Ananyev B. I., “State estimation for linear stochastic differential equations with uncertain disturbances via BSDE approach”, AIP Conference Proceedings, 1487 (2012), 143–150 | DOI

[10] Ananev B. I., “Minimaksnaya kvadratichnaya zadacha korrektsii dvizheniya”, Prikl. matematika i mekhanika, 41:3 (1977), 436–445 | MR

[11] Jin Ma, Protter P., Yong J. M., “Solving forward-backward stochastic differential equations explicitly – a four step scheme”, Probab. Theory Related Fields, 98:3 (1994), 339–359 | DOI | MR | Zbl

[12] Bouchard B., Touzi N., “Discrete-time approximation and Monte Carlo simulation of backward stochastic differential equations”, Stochastic Process. Appl., 111 (2004), 175–206 | DOI | MR | Zbl