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Fourier series associated with the sample functions of a stochastic process

Published online by Cambridge University Press:  24 October 2008

G. Samal
G. Samal
Affiliation:
Department of Mathematics, Ravenshaw College, Cuttack 3, Orissa, India
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Extract

We consider a stochastically continuous process ω(t, α) with independent increments, whose sample functions are bounded in the unit interval 0 ≤ t ≤ 1 for almost all α. If ω(t, α) is a process with independent increments, the characteristic function of ω(t, α) is of the form exp {tψ(u)} where where F is a σ-finite measure with finite mass outside every neighbourhood of o, and a and σ are constants. There is no essential restriction in supposing ω(0, α) = 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 101 - 106
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Cramer, H.Random variables and probability distribution. Cambridge Tracts in Mathematics. No. 36, (Cambridge University Press, 1937).Google Scholar
(2)Gikhman, & Skorohod, . Introduction to the theory of random processes (In Russian), Izdatelstvo Nauka (Moscow, 1965).Google Scholar
(3)Gnedenko, B. V. & Kolmogorov, A. N.Limit distributions for sums of independent random variables (Addison-Wesley, Inc., 1954).Google Scholar
(4)Samal, G. Ph.D. thesis, London University (1961).Google Scholar