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Continuity of stochastic convolutions
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UNSPECIFIED (2001) Continuity of stochastic convolutions. CZECHOSLOVAK MATHEMATICAL JOURNAL, 51 (4). pp. 679-684. ISSN 0011-4642.
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Abstract
Let B be a Brownian motion, and let C-P be the space of all continuous periodic functions f: R --> R with period 1. It is shown that the set of all f is an element of C-P such that the stochastic convolution X-f,X-B(t) = integral(0)(t) f(t - s) dB(s), t is an element of [0, 1] does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | CZECHOSLOVAK MATHEMATICAL JOURNAL | ||||
Publisher: | CZECHOSLOVAK MATHEMATICAL JOURNAL | ||||
ISSN: | 0011-4642 | ||||
Official Date: | 2001 | ||||
Dates: |
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Volume: | 51 | ||||
Number: | 4 | ||||
Number of Pages: | 6 | ||||
Page Range: | pp. 679-684 | ||||
Publication Status: | Published |
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