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Commentationes Mathematicae Universitatis Carolinae

Eugene Seneta The principle of truncations in applied probability
Commentationes Mathematicae Universitatis Carolinae, Vol. 9 (1968), No. 2, 237--242

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Commentationes Mathematicae Universitatia Carolinae 9 f 2 (1968) THE PRINCIPLES OP TRUNCATIONS IN APPLIED PROBABILITY * E. SENETA, Canberra

!• The Principle of Truncations The "principle of truncations" in general may be stated as follows: "To solve an infinite system of linear equations in an infinite number of unknowns, one limits the system to i the first n n equations, and in it neglects all but the first unknowns. The solutions of these systems tend, as

to the required solution". A history of this principle up to 1913 is contained in Chs.I and II of Riesz (1913), from which work the contents of the present section are taken. ^be use of the idea appears to go right back to Fourier (Tfoe Analytical Theory of Heat)who obtained a correct answer, as did several subsequent workers, without actual justifica­ tion. The legitimacy of the method was first investigated by Poincar^, who showed that if the matrix A vector c of the system under consideration and the infinite

(1.1)

A* - c C Ł в . ^ O í j * * * " %,

-i= -f,--, .. )

satisfy extremely strict conditions, the principle is valid. The problem is closely connected to the problem of \p~

• An expository article,read at the 1967 meeting of the Aur talian Mathematical...