Wave equation for a homogeneous string with fixed ends driven by a stable random noise

Averaging principle for a stochastic cable equation

“…In [2] the ergodic property of the solution to a fractional stochastic heat equation is established. Wave equations with general stochastic measures and α-stable distributions are investigated in the papers [5,7,8,24] and [20,29,19], respectively.…”

“…− s) 3/2n≥2 (1 + n) 2 L 2 e − (2n−1) 2 L 2 4(t−s)ds. (35)Then we use the same reasoning as in getting(29) and haven≥2 (1 + n) 2 L 2 e − (2n−1) 2 L 2 4(t−s) ≤ C4(t − s). | ≤ Ch β(σ ) .The same estimate holds for term |I 1+ | ≤ Ch β(σ ) .…”