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| Title: | Marginal Distributions of Self-Similar Processes with Stationary Increments |
| Authors: | O'Brian, George
Vervaat, Wim |
| Keywords: | self-similar processes
stationary increments
marginal distributions
concentration function
continuity of distribution functions
tails |
| Issue Date: | 2-Jul-2009 |
| Series/Report no.: | 550 |
| Abstract: | Let X= (Xt)t more than or equal to 0 to be a real-valued stochastic process which is self-similar with exponent H>0 and has stationary increments. Several results about the marginal distribution of X1 are given. For H inequal to 1, there is a universal bound, depending only on H, on the concentration function of logXsuper+sub1. For all H>0, X1 cannot have any atoms except in certain trivial cases. Some lower bounds are given for the tails of the distribution of X1 in case H>1. Finally, some results are given concerning the connectedness of the support of X1. |
| Description: | Vervaat was a visitor from Katholieke Universiteit. Technical report dedicated to Professor John Lamperti in recognition of his pioneering work in this field. |
| URI: | http://hdl.handle.net/1813/13090 |
| Appears in Collections: | ORIE Technical Reports
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