Sentence examples for principles for stochastic from inspiring English sources

Budhiraja et al. [14] studied the moderate deviation principles for stochastic differential equations driven by a Poisson random measure in finite and infinite dimensions.

First, the essential dynamics of such systems may be hard to discern, and model reduction based on first principles for stochastic systems on complex networks is difficult.

Wang and Zhang [13] established the moderate deviation principle for stochastic reaction-diffusion equations.

With the developing of stochastic analysis theory, many authors began to study the averaging principle for stochastic differential equations (SDEs).

Xu, Duan, and Xu [4] established an averaging principle for stochastic differential equations with general non-Gaussian Lévy noise.

In this paper, we investigate the averaging principle for stochastic delay differential equations (SDDEs) and SDDEs with pure jumps.

With the developing of the theory of stochastic analysis, many authors began to study the averaging principle for stochastic differential equations (SDEs).

Instead of Poisson noise, Xu et al. [7] established an averaging principle for stochastic differential equations with general non-Gaussian Lévy noise.

It was first introduced by Khasminskii [13] in 1968, and since then, the principle for stochastic differential equations was intensively and extensively studied.

Pei et al. [46] considered the averaging principle for stochastic hyperbolic- parabolic equations driven by Poisson random measures with slow and fast time-scales.

LaSalle-type invariance principle for stochastic differential delay equations is employed to investigate the globally almost surely asymptotical stability of the error dynamical system.