Box dimension of interpolations of self-similar processes with stationary increments (Q2772073)
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scientific article; zbMATH DE number 1706615
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Box dimension of interpolations of self-similar processes with stationary increments |
scientific article; zbMATH DE number 1706615 |
Statements
18 February 2002
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fractal interpolation
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interpolation dimension
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box dimension
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self-similar process
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stationary increments
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stable processes
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Box dimension of interpolations of self-similar processes with stationary increments (English)
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For \(H\)-sssi processes four kinds of convergence of interpolation dimensions are discussed. It is shown that under a rather general condition they converge in probability to \(2-H\). Furthermore, it is shown that for an \(H\)-sssi process with continuous sample paths under the same condition the sample paths of fractional interpolations converge in probability to sample paths of the interpolated process.
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