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S. Dharmadhikari, V. Fabian, K. Jogdeo (1968)
Bounds on the Moments of MartingalesAnnals of Mathematical Statistics, 39
V. Sazanov (1975)
On the Estimation of Moments of Sums of Independent Random VariablesTheory of Probability and Its Applications, 19
A. Novikov (1973)
On an Identity for Stochastic IntegralsTheory of Probability and Its Applications, 17
D. Kh. Fuk (1973)
Certain probability inequalities for martingalesSib. Mat. Zh., 14
A. Novikov (1975)
On Discontinuous MartingalesTheory of Probability and Its Applications, 20
V. V. Yurinskii (1974)
Exponential estimates for large derivationsTeor. Veroyatn. Ee Primen., 19
S. Dharmadhikari, K. Jogdeo (1969)
BOUNDS ON MOMENTS OF CERTAIN RANDOM VARIABLESAnnals of Mathematical Statistics, 40
V. M. Zolotarev (1977)
Ideal metrics in the problem of approximation of distributions of sums of independent random variablesTeor. Veroyatn. Ee Primen., 22
I. F. Pinelis (1978)
On the distribution of sums of independent random variables with values in a Banach spaceTeor. Veroyatn. Ee Primen., 24
A. A. Novikov (1972)
On an identity for stochastic integralsTeor. Veroyatn. Ee Primen., 17
A. A. Novikov (1977)
On discontinuous martingalesTeor. Veroyatn. Ee Primen., 20
S. V. Nagaev, I. F. Pinelis (1977)
On large deviations for sums of independent random variables with values in a Banach spaceTheses of Reports of the Second Vilnius Conference on Theory of Probability and Mathematical Statistics [in Russian], 2
I. Pinelis (1979)
On the Distribution of Sums of Independent Random Variables with Values in a Banach SpaceTheory of Probability and Its Applications, 23
V. V. Sazonov (1974)
On the estimation of moments of sums of independent random variablesTeor. Veroyatn. Ee Primen., 19
S. V. Nagaev, I. F. Pinelis (1977)
Some inequalities for distributions of sums of independent random variablesTeor. Veroyatn. Ee Primen., 22
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
Mathematical Notes – Springer Journals
Published: Jan 28, 2005
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