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Estimates of moments of infinite-dimensional martingales

Estimates of moments of infinite-dimensional martingales A detailed investigation of the general scheme of partial averaging considered for the case of differential equations is given in [8]. Theorem 1 gives a justification for various averaging schemes for controlled systems (see [6, 7, i0]) 2 : e/ (t, x, u), x (0) ~ x ~ (24) where u (t)~ U~W n is the control vector. Indeed, inclusion (i) corresponds to system (24) for X(t, x) ~ f(t, x, U). LITERATURE CITED i. A. N. Pilatov, "On partial averaging for systems of ordinary differential equations," Diff. Uravn., 6, No. 6, 1118-1120 (1970). 2. A. N. Filatov, Averaging Methods in Differential and Integrodifferential Equations [in Russian], Fan, Tashkent (1971). 3. A. N. Filatov, Asymptotic Methods in the Theory of Differential and Integrodifferential Equations [in Russian], Pan, Tashkent (1974). 4. A. N. Filatov and L. V. Sharova, Integral Inequalities and Theory of Nonlinear Oscilla- tions [in Russian], Nauka, Moscow (1976). 5. V. G. Zadorozhnyi, "The Krylov--Bogolyubov averaging method in the Carath~odory Condi- tions," Tr. Mat. Fakul'teta Voronezhsk. Univ., No. 7, 60-68 (1972). 6. V. A. Plotnikov, Asymptotic Methods in Problems of Optimal Control [in Russian], Izd. Odessk. Gos. Univ. (1976). 7. V. A. Plotnikov, "The partial-averaging method in problems http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Notes Springer Journals

Estimates of moments of infinite-dimensional martingales

Mathematical Notes , Volume 27 (6) – Jan 28, 2005

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References (15)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-4346
eISSN
1573-8876
DOI
10.1007/BF01145436
Publisher site
See Article on Publisher Site

Abstract

A detailed investigation of the general scheme of partial averaging considered for the case of differential equations is given in [8]. Theorem 1 gives a justification for various averaging schemes for controlled systems (see [6, 7, i0]) 2 : e/ (t, x, u), x (0) ~ x ~ (24) where u (t)~ U~W n is the control vector. Indeed, inclusion (i) corresponds to system (24) for X(t, x) ~ f(t, x, U). LITERATURE CITED i. A. N. Pilatov, "On partial averaging for systems of ordinary differential equations," Diff. Uravn., 6, No. 6, 1118-1120 (1970). 2. A. N. Filatov, Averaging Methods in Differential and Integrodifferential Equations [in Russian], Fan, Tashkent (1971). 3. A. N. Filatov, Asymptotic Methods in the Theory of Differential and Integrodifferential Equations [in Russian], Pan, Tashkent (1974). 4. A. N. Filatov and L. V. Sharova, Integral Inequalities and Theory of Nonlinear Oscilla- tions [in Russian], Nauka, Moscow (1976). 5. V. G. Zadorozhnyi, "The Krylov--Bogolyubov averaging method in the Carath~odory Condi- tions," Tr. Mat. Fakul'teta Voronezhsk. Univ., No. 7, 60-68 (1972). 6. V. A. Plotnikov, Asymptotic Methods in Problems of Optimal Control [in Russian], Izd. Odessk. Gos. Univ. (1976). 7. V. A. Plotnikov, "The partial-averaging method in problems

Journal

Mathematical NotesSpringer Journals

Published: Jan 28, 2005

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