Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process
Strong and weak convergence rates for slow–fast stochastic differential equations driven by α-stable process
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DOI：
10.3150/21-bej1345
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发表时间：
2022-02
期刊：
影响因子：
1.5
通讯作者：
Xiaobin Sun;Longjie Xie;Yingchao Xie
中科院分区：
文献类型：
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作者：
Xiaobin Sun;Longjie Xie;Yingchao Xie
涉及“慢”和“快”分量的多尺度模型自然地出现在各种领域中，诸如非线性振荡、化学动力学、生物学、气候动力学等，参见，例如，[23][24][25][26][27][28][29]多尺度模型的平均原理描述了当尺度参数→ 0时慢分量的渐近行为。在[23]中，Khasminskii考虑了一类由Wiener噪声驱动的多尺度随机微分方程，即，dXt = A（Xt，Yt）dt+ dWt，X0 = x ∈ R，dYt = 1 B（Xt，Yt）dt+ 1 dWt，Y0 = y ∈ R，
Multiscale models involving “slow” and “fast” components appear naturally in various fields, such as nonlinear oscillations, chemical kinetics, biology, climate dynamics, etc, see, e.g., [3,12,22,33] and the references therein. The averaging principle of multiscale models describes the asymptotic behavior of the slow components as the scale parameter → 0. In [23], Khasminskii considered a class of multiscale stochastic differential equations (SDEs for short) driven by Wiener noise, i.e., dX t = A(X t , Y t )dt+ dWt, X 0 = x ∈ R, dY t = 1 B(X t , Y t )dt+ 1 √ dWt, Y 0 = y ∈ R,