The Gaussian-Volterra process with a linear kernel is considered, its properties are established and projection coefficients are explicitly calculated, i.e. one of possible prediction problems related to Gaussian processes is solved.
We consider the cable equation in the mild form driven by a general stochastic measure. The averaging principle for the equation is established. The rate of convergence is estimated. The regularity of the mild solution is also studied. The orders in time and space variables in the Holder condition for the solution are improved in comparison with previous results in the literature on this topic.