The null hypothesis is stated that asset "A"

stochastically dominates over asset "B", whereas, the alternative hypothesis implies that distribution B

stochastically dominates over A.

The rainfall depths were

stochastically generated using a two-component extreme value distribution (describing the effect of two different meteorologic factors) for a fixed duration, and regionalised through a cluster analysis.

Since we have established that [p.sup.H] > [p.sup.h] and [p.sup.L] > [p.sup.l], we can conclude that [F.sub.M] and [F.sub.O]

stochastically dominate F for any price below [p.sup.L] or above [p.sup.h].

In case [M.sub.BH] = const, then <J(x,x')> depends on the dimensionality of the internal Hilbert space of the black hole and thus fluctuates

stochasticallyLet [psi] : [[summation].sup.n] [right arrow] [[bar.M].sup.n+1] be a

stochastically complete constant f-mean curvature [H.sub.f] spacelike hypersurface such that sup h [greater than or equal to] [h.sub.0], inf h [less than or equal to] [h.sub.0] which is contained in a slab; then [[summation].sup.n] is f -maximal.

It follows that the GkNN process is

stochastically dependent on {[v.sub.t] : t = 1,2, ...} with kernel K defined by

It can be concluded from Definition 5 that the system is

stochastically stable, and the proof is completed.

In Panel B of Table II, we use

stochastically detrended aggregate relative effective bid-ask spread, LRES_SD, as an alternative illiquidity measure and find qualitatively similar results.

The motivation for the model studied in that reference is the fact that the simple branching process in which immigration can occur is

stochastically monotone; see (3) in [3].

The sufficient and necessary conditions which make the closed-loop system

stochastically stable and achieve prescribed [H.sub.[infinity] performance are derived in Section 3.

Then, CNN (1) is

stochastically exponentially mean square stable if the following condition holds:

For some given constants [c.sub.1] > 0, [delta] > 0, and T > 0 and symmetric matrix W > 0, system (5) with [omega](t) [equivalent to] 0 is said to be mean-square

stochastically finite-time stable (MSSFTS) with respect to ([c.sub.1],[c.sub.2], [delta], T, W), if there exist constants [c.sub.2] > [c.sub.1], such that