Sentence examples for sure limit from inspiring English sources

The almost sure limit theorems are established under the assumption that the associated Schrödinger operator of X has a spectral gap.

For H<12, we prove existence and positivity of the Lyapunov exponent defined as the almost sure limit limt→∞t−1logu(t).

We establish almost sure limit theorems for a branching symmetric Hunt process in terms of the principal eigenvalue and the ground state of an associated Schrödinger operator.

In the IMAP Access section, under Folder Size Limits make sure Limit IMAP folders to contain no more than this many messages is selected, then choose the preferred limit from the drop-down menu.

When the underling process is a symmetric diffusion with C1b-coefficients or a symmetric Lévy process on Rd whose Lévy exponent Ψ is bounded from below by c|η|α for some c>0 and α∈ 0,2) when |η| is large, a stronger almost sure limit theorem is established for the superprocess.

Recently Gonchigdanzan and Rempala [9] obtained the almost sure limit theorem related to (1) as follows.

There are, to be sure, limits to Charles's revolutionism.

For H>12, we prove that the upper and lower almost sure limits limsupt→∞t−2Hlogu(t) and liminft→∞(t−2Hlogt)logu(t) are non-trivial in the sense that they are bounded respectively above and below by finite, strictly positive constants.

Peng et al. [12] studied the almost sure limiting behavior for partial sums and maxima of i.i.d.i.d

The almost sure limiting behavior of weighted sums was studied by many authors; see, for example, Choi and Sung [10], Cuzick [11], Wu [12], and Sung [13, 14], and so forth.

Although we have noticed that many network models belong to this model class, this restriction on the topology for sure limits the use of our approach.