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Published online by Cambridge University Press: 24 October 2008
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.
