Yamnenko R. Investigation of the storage processes from Orlicz spaces.

The dissertation is devoted to the investigation of properties of extremal functionals from random processes in Orlich spaces of exponential type. The rate of convergence of wavelet decompositions of generalized random processes from Orlich spaces, trajectories of which belong to the L2(Ω) space, is investigated. It is shown that the convergence rate of wavelet decompositions Xn(t) has the order of o(1/2n) or O (1/2n) as under some additional conditions on wavelet bases. Estimates of the probabilities that a mixture of independent random processes from Orlich spaces of exponential type, in particular, from the class V(φ,ψ), will exceed the level specified by some continuous function, are generalized. Examples of application to the problems from queuing theory and financial mathematics using generalized processes of fractional Brownian motion and Ornstein-Uhlenbeck are given. For the first time, Poisson sums with φ-sub-Gaussian random terms are studied. Estimates of the probability of exceeding by such sums the level, given by some continuous monotonically increasing function, are obtained. For sub-Gaussian risk processes, the probability of bankruptcy is estimated. The properties of accumulation processes from Orlich spaces of exponential type are investigated, in particular, the conditions of boundedness and estimates of the exponential moment of accumulation processes are obtained. Estimates of the distribution of functionals of extremum type characterizing the storage processes from Orlich spaces of exponential type are obtained. The properties of γ-reflected random processes with an input process from some Orlich spaces of exponential type, in particular of the class V(φ,ψ) are investigated, an estimate of the probability of bankruptcy of the corresponding model is obtained. The behavior of the norms of sub-Gaussian random processes, influenced by a certain measurable function in Orlich spaces, in particular, in the space Lp(T) , is studied. The distribution of norms of deviations of sub-Gaussian random processes from a given function in Orlich spaces is estimated using the method of majorizing measures, and the distribution of the supremum of the averaged deviations of the random process from the Orlich spaces of random variables is investigated.