Fourier series associated with the sample functions of a stochastic process
Published online by Cambridge University Press: 24 October 2008
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.
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- 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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