Sentence examples for bounds similar from inspiring English sources

Reminding that L is a sum of N independent random variables, asymptotic analysis in probability theory (when N is large enough) shows that bounds similar to (24) and (25) are much more appropriate for estimating α and β than the Gaussian approximation especially when λ is far from E[L], namely when bounding the tails of a distribution [16, 17].

We adjust the price of the provider such that the risk of a financial loss is bounded similar to the Value-at-Risk (VaR).

Since { f ( s, x ( s ), ( H x ) ( s ) ) } ⊆ L p 2 ( I, X β ) is bounded, similar to the proof of Theorem 3.2, it is easy to see that ∥ ( Q 1 x ) ( t ) ∥ α is bounded.

The only general results known so far for the stability of the stationary solutions are those of Atay and Hutt (see, for example, [20]): they found a bound similar to condition 2 in Proposition 3.15 by using the CVs, but no proof of stability was given.

But the inequality (9) will be replaced by ∥ 2 n f ( x 2 ) − f ( x ) ∥ ≤ 2 n τ ( x 2 ) for all x ∈ X, which will ends up at a bound similar to (10), that is, ∥ 2 m n f ( 2 − m x ) − f ( x ) ∥ ≤ ∑ i = 1 ∞ 2 i n τ ( 2 − i x ).

As expected, the mutual information exhibits a similar increase with increasing PCD with no upper bound, similar to the SNR analysis.

The new approach approximates the stochastic noise as a bounded uncertainty, similar to having bounds in the control charts for stochastic process control data.

Comparing the error bounds for similar and dissimilar DNA motifs shows that the approximation for similar DNA motifs yields large bounds.

Estimating the LSMN/L C/VFAs and their associated lower bounds takes similar computational effort.

Therefore, some conditions are necessary to make these bounds redundant, similar to the ones in (30 - 33 30 - 33

The derivative bounds have similar decrease properties as a function over G, the correct singularity as a function of t, and also reflect the joint analyticity of K.