Continuity of stochastic convolutions
UNSPECIFIED. (2001) Continuity of stochastic convolutions. CZECHOSLOVAK MATHEMATICAL JOURNAL, 51 (4). pp. 679-684. ISSN 0011-4642Full text not available from this repository.
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|
|Subjects:||Q Science > QA Mathematics|
|Journal or Publication Title:||CZECHOSLOVAK MATHEMATICAL JOURNAL|
|Publisher:||CZECHOSLOVAK MATHEMATICAL JOURNAL|
|Number of Pages:||6|
|Page Range:||pp. 679-684|
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