stochastic

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Related to stochastically: Stochastically independent

stochastic

[stō′kas·tik]
(mathematics)
Pertaining to random variables.

stochastic

stochastic

By guesswork; by chance; using or containing random values.
References in periodicals archive ?
In this context, asset "a" stochastically dominates over asset "6" by second order if and only if the following condition is satisfied.
Another early application is by Beran (1973), whom stochastically sampled both the storm depth and duration to estimate flood frequencies.
In the case where a mixed strategy equilibrium prevails both before and after the merger, the postmerger price distribution of each firm stochastically dominates its premerger counterpart.
Note that, at constant r from the horizon, the energy density of the vacuum fluctuations depends on the internal degrees of freedom of the black hole and varies stochastically.
Let ([M.sup.n], (,), [e.sup.-f]dM) be an n-dimensional stochastically complete weighted Riemannian manifold and u : M [right arrow] R be a smooth function which is bounded from below on [M.sup.n].
We will show that the process {[y.sub.1], [y.sub.2], ...} is stochastically dependent on the time series {v t : t = 1,2, ...}.
Then the closed-loop system (16) is stochastically stable with the dynamic feedback controller.
LRES_LD (LRES_SD) is linearly (stochastically) detrended aggregate relative effective spread.
We shall see in the next section that F(t) is stochastically monotone; that is, [[summation].sub.k[greater than or equal to]j] [f.sub.ik](t) is nondecreasing in i, for each j.
Compared to the previous relevant works, the main contribution of this paper is that, for the Markov jump NCSs, the sufficient and necessary conditions for the stochastically stability of the closed-loop system are derived, and the method of calculating the minimal [H.sub.[infinity] attenuation [[gamma].sub.min] is obtained by constructing proper Lyapunov function candidate.
Holder inequality, Burkholder-Davis-Gundy inequality, and the continuous semigroup of Laplace operators to derive the stochastically exponential stability criterion of the complex system.
By applying the finite-time theory and constructing appropriate mode-dependent Lyapunov-Krasovskii functionals, the resulting closed-loop system can be stochastically finite-time bounded with the prescribed passivity performance level.