Journal article
Wave Equation For A Homogeneous String With Fixed Ends Driven By A Stable Random Noise
Year:
2019Published in:
Theory of Probability and Mathematical StatisticsWave equation for a string
wave equation
Fourier method
generalized solution
stable measure with independent increments
LePage representation
A wave equation with external forces is considered in this paper for a homogeneous string with fixed ends. The distribution of the right-hand side of the equation is symmetric α-stable. It is proved that the function constructed by the Fourier method is a generalized solution of the equation. The regularity of the trajectories is also established.