Kamenschykova O. Approximation of random processes with given accuracy and reliability

Estimates of increments of periodic random Lp(omega)-process in metrics of Lq[a,b], for different relations between numbers p,q, are obtained in the dissertation. Approximations of periodic random Lp(omega)-processes by means of trigonometric functions in the metrics of Lq[0,2pi] are constructed. Estimate of the distribution of increments of the Orlicz process in the metrics of C[0,infinity) is found. The approximation of Orlicz processes in the metrics of C[0,infinity), by the means of integer functions of the exponential type no more than some gamma>0 is constructed. Problems of approximation of strictly phi-sub-Gaussian processes by means of broken lines, Bernstein polynomials and cubic splines, in the metrix of Lp(0,T) and C(0,T), are studied.