Sentence examples for bounded by some random from inspiring English sources
Theorem A Let { X n k, 1 ≤ k ≤ n, n ≥ 1 } be an array of rowwise independent random variables with E X n k = 0. Suppose that { X n k, 1 ≤ k ≤ n, n ≥ 1 } are uniformly bounded by some random variable X.
The dynamic uncertainties are bounded by some norm, that is usually normalized by unity.
Spans: NomBank arguments are mostly bounded by some syntactic element in the Penn Treebank annotation.
The random variables { X k, k ∈ Z + d } are said to be weakly bounded by the random variable ξ if there exist some constants c 1, c 2 > 0, n 0 ∈ Z + d and x 0 > 0 such that for every x > x 0 and n ≥ n 0, n ∈ Z + d c 1 P ( | ξ | > x ) ≤ 1 | n | ∑ k ≤ n P ( | X k | > x ) ≤ c 2 P ( | ξ | > x ).
Let ({X_{n}, ngeq1}) be a sequence of random variables weakly upper bounded by a random variable X.
If ({X_{n}, ngeq1}) is coordinatewise weakly bounded by a random vector X satisfying (2.11) and (2.12), then (3.1) holds.
If ({X_{n}, ngeq1}) is coordinatewise weakly upper bounded by a random vector X, then (3.1) implies (2.4).
Let ({X_{n}, ngeq 1}) be a sequence of (mathbb{R}^{d} -valued randomathbb{R}^{d} -valuedrandomded by a random vectorsX, and let (r>0).
If ({X_{n}, n geq 1}) is coordinatewise weakly upper bounded by a random vector X with (sum_{j=1}^{d} Evert X^{(j)} vert
If ({X_{n}, ngeq 1}) is weakly upper bounded by a random
