Abstract
Averaging principle for a stochastic cable equation
Highlights
Averaging methods are important for describing and investigating the asymptotic behavior of dynamical systems
We consider the cable equation in the mild form driven by a general stochastic measure
The averaging principle for fractional differential equations driven by Lévy noise is established by Shen et al [31]
Summary
Averaging methods are important for describing and investigating the asymptotic behavior of dynamical systems. The averaging principle for equations driven by general stochastic measures is considered in [6, 22, 23, 26, 30]. Our aim here is to establish the averaging principle for the cable equation driven by stochastic measure studied in [25]. For this purpose we improve the orders of the Hölder condition for the mild solution with respect to space and time variables obtained in [25, Theorem 5.1] (see Theorem 1 below).
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