Sentence examples for bounded by a random from inspiring English sources

Suppose that ({ X_{n},ngeq1}) is coordinatewise weakly upper bounded by a random vector 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 upper bounded by a random vector X, then (3.1) implies (2.4).

If ({X_{n}, ngeq1}) is coordinatewise weakly bounded by a random vector X satisfying (2.11) and (2.12), then (3.1) holds.

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).

Suppose that ({X_{n}, ngeq1}) is coordinatewise weakly bounded by a random vector X with sum_{j=1}^{infty}E bigl( biglvert X^{(j)} bigrvert ^{r}I bigl( biglvert X^{(j)} bigrvert leq1 bigr) bigr)< infty.

Also, X n (r)≤1 for all r, and so |X n (r)| is bounded by an integrable random variable.

More precisely, our error estimate has an a priori and an a posteriori aspect: With a priori overwhelming probability, the (random) prefactor can be bounded by a constant that is computable without much further effort, on the basis of the given realization in the box of size $L$.

Moreover, we proposed an average-case linear time algorithm, under the assumption that the number of indels is bounded by a constant and the database structures follow the random-walk model.

Each detected bout is bounded by a red box.

One edge is bounded by a native hedge.