The problem of optimally controlling a Wiener process until it leaves an interval (a; b) for the first time is considered in the case when the infinitesimal parameters of the process are random. When a = ��1, the exact optimal control is derived by solving the appropriate system of differential equations, whereas a very precise approximate solution in the form of a polynomial is obtained in the two-barrier case.

Analysis of power consumption presents a very important issue for power distribution system operators. Some power system processes such as planning, demand forecasting, development, etc.., require a complete understanding of behaviour of power consumption for observed area, which requires appropriate techniques for analysis of available data. In this paper, two different time-frequency techniques are applied for analysis of hourly values of active and reactive power consumption from one real power distribution transformer substation in urban part of Sarajevo city. Using the continuous wavelet transform (CWT) with wavelet power spectrum and global wavelet spectrum some properties of analysed time series are determined. Then, empirical mode decomposition (EMD) and Hilbert-Huang Transform (HHT) are applied for the analyses of the same time series and the results showed that both applied approaches can provide very useful information about the behaviour of power consumption for observed time interval and different period (frequency) bands. Also it can be noticed that the results obtained by global wavelet spectrum and marginal Hilbert spectrum are very similar, thus confirming that both approaches could be used for identification of main properties of active and reactive power consumption time series.