SankhyĀ - The Indian Journal of Statistics

According to the verdict of the official enquiry the accident was due to an error of judgement on the part of the pilot. [...] (3) Kolmogoroff (1933) proved that every stochastic process ; dependinon a continuous parameter t can be realized in the space of all functionsz The realization of ; in the space if of all functions however has considerable disadvantages since in jf.many sets that are of practical interest do not lie in the Borel extension of the cylidrical set's. [...] Theorem 1 : Every stochastic process depending on a continuous parameter can be realized in the space of all functions of Baire class 2. Let the stochastic process xt be realized in if by the measure P. It is easy to verify that conditiOn ft) is equivalent to stating that in the space of all functions the outer P measure of eqtYals one. [...] Thus A = (0.2) The row vectors in A are represented by an and the column vectors by The rank of the matrix A is equal to the number of independent vectors in the a set which is same as that in the /3 set. [...] 11 ] SANKHYA : THE INDIAN JOURNAL OF ETATISTiCS PART 1 Calling the larger of M1 and M2 by M and the smaller of ni and pi' by ri(ir---1 2...