Modeling Abstract Stochastic Problems with White Noise Perturbations

摘要

We consider construction of a vibrating string model under the influence of random impulses. The model is obtained in the form of the Cauchy problem for the second order difference equation with a Brownian sheet. Properties of random processes that reflect the stochastic influence are investigated. The connection of the Brownian sheet and its generalized derivative with Hilbert space valued Wiener processes is shown. As a result, the Cauchy problem for the stochastic equation with Ito integral with respect to a Wiener process is obtained.