Results 191 to 200 of about 2,835 (222)

On a Kolmogorov Inequality

Theory of Probability & Its Applications, 1985
Translation from Teor. Veroyatn. Primen. 29, No.2, 382-384 (Russian) (1984; Zbl 0542.60021).
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A Note on a Kolmogorov Inequality for the Binomial Distribution

Theory of Probability & Its Applications, 1989
A sharper inequality for the probability \(P(\sup_{k\geq n}| \bar Y_ k-p| \geq \epsilon)\) is derived, where \(\bar Y_ k=k^{- 1}\sum^{k}_{j=1}Y_ j\), \(\epsilon >0\), and \(Y_ 1,Y_ 2,..\). is a sequence of i.i.d. Bernoulli random variables with mean p, \(0\leq p\leq 1\).
Young, D. M., Turner, D. W., Seaman, J. W.   +2 more
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Landau-kolmogorov-hörmander inequalities on the semiaxis

Mathematical Notes, 1999
The problem of the asymmetric ideal spline least deviating from zero in the \(C[a,b]\)-metric is solved. The authors prove the Landau-Kolmogorov-Hörmander inequalities for the norms of positive and negative parts of intermediate derivatives of functions on the semiaxis that take into account restrictions on the positive and negative part of the higher ...
Babenko, V. F., Kofanov, V. A., Pichugov, S. A.   +2 more
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A Kolmogorov-type inequality

Mathematical Proceedings of the Cambridge Philosophical Society, 2004
A Kolmogorov-type inequality \[ \| Pf\| _ B\leq c\| Qf\| _ B^{m/r}\| f\| _ B^{1-m/r} \] (where ...
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Kolmogorov-type inequalities for derivatives

Sbornik: Mathematics, 1997
By a Kolmogorov type inequality the authors mean an inequality of the following form \[ \| x^{(k)}(\cdot)\| _{L_q(T)} \leq K\| x(\cdot)\| _{L_p(T)}^\alpha \| x^{(n)}(\cdot)\| _{L_r(T)}^\beta, \] (where \(0\leq k\leq n\) are integers, \(1\leq p,q,r\leq\infty\), \(\alpha,\beta\geq 0\), \(T={\mathbb R}\) of \({\mathbb R}_+\)) which must hold for all ...
Magaril-Il'yaev, G. G., Tikhomirov, V. M.   +1 more
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On Constants in the Kolmogorov–Rogozin Inequalities in the Hilbert Space

Journal of Mathematical Sciences, 2023
The author considers Kolmogorov-Rogozin and Kesten inequalities. The values of the absolute constants in these inequalities are refined for the concentration function of the sum of independent random vectors in a Hilbert space.
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On Kolmogorov-Type Inequalities with Integrable Highest Derivative

Ukrainian Mathematical Journal, 2002
Summary: We obtain a new exact Kolmogorov-type inequality for \(2\pi\)-periodic functions \(f\in L_1^r\) and any \(k,r\in\mathbb N ...
Babenko, V. F., Kofanov, V. A., Pichugov, S. A.   +2 more
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Strengthening of the Kolmogorov Comparison Theorem and Kolmogorov Inequality and Their Applications

Ukrainian Mathematical Journal, 2002
We obtain a strengthened version of the Kolmogorov comparison theorem. In particular, this enables us to obtain a strengthened Kolmogorov inequality for functions x ∈ L∞x(r), namely, $$\left\| {x^{(k)} } \right\|_{L_\infty (R)} \leqslant \frac{{\left\| {\phi _{r - k} } \right\|_\infty }}{{\left\| {\phi _r } \right\|_\infty ^{1 - k/r} }}M(x)^{1 - k ...
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Landau-Kolmogorov and Related Inequalities

1991
Let f be a real function with n derivatives on an interval I of the real line. Define $${M_k}(p,I) = \parallel {f^{(k)}}{\parallel _p},\quad 0 \leqslant k \leqslant n.$$
D. S. Mitrinović, J. E. Pečarić, A. M. Fink   +2 more
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Strengthening of Kolmogorov Type Inequalities for Derivatives and Differences

Journal of Mathematical Sciences, 2019
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