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Download Topics in the Theory of Random Noise Vol 2 by R L Stratonovich PDF

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By R L Stratonovich

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328-338. 338 Reprinted from the Annals of Mathematical Statistics, Vol. 13, No. 3, 1942. 31 32 MUTUALLY FAVORABLE EVENTS 339 U v(vi i "2) = P W , we say that En is indifferent to E„2 . „2 . Thus the relations "favorableness," "indifference," and "unfavorableness" are mutually exclusive and together exhaustive. We state the following immediate consequences: (i) Refiexity: An event is favorable to itself; in fact, p(v, v) = 1 > p(v). (ii) Symmetry: If Ex is favorable (indifferent, unfavorable) to E2, then E2 is favorable (indifferent, unfavorable) to Ex.

R_l)'r = Pl---r, by an easy modification of Poincare's formula. Next consider a fixed p ^ r + 1. iM-i)'/i, where Qii, • • • , jus) is a combination out of (1, • • • , r); and it appears exactly once with the sign (—1)\ Their total contribution is therefore — P(r+l)'---((i-l)V + 2rf V'l (>•+«'• ••(JI-D'JI — Z-i P»;>'i(r+»'---(M-l)'/i + - - ' J-l >'lt»'2 + ( by another application r + 1, • • • , n, we obtain (19) — \r-1 1 ) ' Pl'---(M+U'd of Poincare's formula. — ( p i . . r ( r + l ) + Pl... r ( r +l)'(r + 2) + ••• + = ~~ Pl"-r(r+l)'---Gu-l)' M > Summing up for /J.

207-209. , Vol. 183 (1941), p . 103. Postscript. This paper was a "take-off" of an earlier one cited in footnote 3) above. The latter was my first non-Chinese publication written c. 1940, after seeing Rohrbach's paper in the Crelle journal in a little reading room where some current periodicals were on display, in Kunming China. Later in 1958,1 took a Rhine river boat from Koblenz to Mainz to visit Rohrbach. Owing to low tide I arrived too late to be met at the wharf. The Rohrbachs gave me a very kind reception.

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