The phrase "average and stochastic" is correct and usable in written English.
It can be used in contexts related to statistics, mathematics, or data analysis, where you are discussing both typical values (average) and random processes (stochastic).
Example: "In our analysis, we will consider both the average and stochastic elements of the data to provide a comprehensive overview."
Alternatives: "mean and random" or "typical and probabilistic".
Jiang et al. [16] showed the stability in time average and stochastic permanence of a non-autonomous logistic equation with random perturbation.
For the results related to the probabilistic, average and stochastic widths, the reader may be referred to Sul'din [1, 2], Traub et al. [3], Maiorov [4 7], Mathé [8 12], Sun [13, 14], and Ritter [15].
For example, the problems of probabilistic, average and stochastic widths, which can reflect the behavior of function on the whole class and give information about the measure of the elements in the class that can be approximated to this or that degree, are the problems of this kind.
These results combine ideas from singular perturbations, classical periodic averaging and stochastic averaging principles.
However, if sperm competitive ability is heritable, females A and B will benefit through the offspring sired by male M because of the inheritance of high absolute sperm competitive ability that will confer, on average and despite stochastic influences (contingent on the distribution of sperm competitiveness in the population of males), high fertilization success.
The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system.
Moreover, the convergence behavior of VFxlogCLMP for moving average secondary paths and stochastic input signals is performed.
Two approaches, multiple time scaling and stochastic averaging, are used.
Combining ideas of periodic and stochastic averaging introduced previously, we present here theoretical results concerning multiscale SDEs driven by an external time-periodic input.
The case 0 < μ < ∞ is already very rich in the sense that it combines simultaneously both the periodic and stochastic averaging principles in a new way that cannot be recovered by sequential applications of those principles.
However, the study of the sequential limits ϵ 1 → 0 followed by ϵ 2 → 0 or ϵ 2 → 0 followed by ϵ 1 → 0 can be deduced from an appropriate combination of classical periodic and stochastic averaging theorems: .
