By Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay K. Rohatgi (eds.)
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Extra resources for Analytical Methods in Probability Theory: Proceedings of the Conference Held at Oberwolfach, Germany, June 9–14, 1980
R6v@sz, P. (1979). Carleton Mathematical Series to appear. ity tests. No. 162. , S e s h a d r i , V. and Y a l o v s k y , M. (1975). Applications of c h a r a c t e r i z a t i o n s in the a r e a of g o o d n e s s - o f - f i t . In Statistical Distributions in S c i e n t i f i c Work, Vol. 2, 79-90, eds. P. P a t i l et al. D. , D o r d r e c h t Holland.  Foutz, R o b e r t empirical V. (1979). probability A test for g o o d n e s s - o f - f i t measure. To appear. based on an A THEOREM OF DENY WITH APPLICATIONS Laurie TO CHARACTERIZATION PROBLEMS Davies Fachbereich Mathematik Universit~t Essen GHS 4300 Essen A t h e o r e m o f D e n y is s t a t e d a n d a p p l i c a t i o n s ization problems are indicated.
This shows that J Since [~(t)] is ergodic, hence T is ergodic. To relate these results back to our original problem, define the real-valued function h on ~ by h(w(1),w (2)) = (w(1)(0),w~ 2)) = [ ~(0, w (i)) ,y0(w (2)) ]. Then it is straightforward to verify that h[T(w(1),w(2))] = [~(yl(w(2)),w(1)),yl(w(2))] or hT = [~(YI),YI] = (ZI,YI) , and in general hT n = [~(~n),Yn] = (Zn,Yn). Thus we have 22 THEOREM 2. d, positive random variables satisfying A2 and A3, then the [(Zn,Yn) ] process is erg0dic and we can estimate consistently all joint probabilities of the [~(t)] process b_~ means of observation of the [(Zn,Yn) ] process.
Of and probability the proof zero where of Deny's (14) theorem 41 REFERENCES [i] Choquet, G. and Deny, J. Sur ......... l ' ~ q u a t i o n de c o n v o l u t i o n = ~ ~. R. Sc. Paris t. L. and Shimizu, R. On identically d i s t r i b u t e d linear statistics, Annals of I n s t q S t a t i s t . M a t h . , 2 8 , (1976),469-489  Deny, J. Sur l ' ~ q u a t i o n de c o n v o l u t i o n ~=~ ~ o. Semin. Theor. Sci. ann.  Feller, W. An i n t r o d u c t i o n to p r o b a b i l i t y theory and its applications, V0i.
Analytical Methods in Probability Theory: Proceedings of the Conference Held at Oberwolfach, Germany, June 9–14, 1980 by Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay K. Rohatgi (eds.)