| Title:
|
Continuity of stochastic convolutions (English) |
| Author:
|
Brzeźniak, Zdzisław |
| Author:
|
Peszat, Szymon |
| Author:
|
Zabczyk, Jerzy |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
679-684 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $B$ be a Brownian motion, and let $\mathcal C_{\mathrm p}$ be the space of all continuous periodic functions $f\:\mathbb{R}\rightarrow \mathbb{R}$ with period 1. It is shown that the set of all $f\in \mathcal C_{\mathrm p}$ such that the stochastic convolution $X_{f,B}(t)= \int _0^tf(t-s)\mathrm{d}B(s)$, $t\in [0,1]$ does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category. (English) |
| Keyword:
|
stochastic convolutions |
| Keyword:
|
continuity of Gaussian processes |
| Keyword:
|
Gaussian trigonometric series |
| MSC:
|
60G15 |
| MSC:
|
60G17 |
| MSC:
|
60G50 |
| MSC:
|
60H05 |
| idZBL:
|
Zbl 1001.60056 |
| idMR:
|
MR1864035 |
| . |
| Date available:
|
2009-09-24T10:46:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127679 |
| . |
| Reference:
|
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| Reference:
|
[2] K. De Leeuw, J.-P. Kahane and Y. Katznelson: Sur les coefficients de Fourier des fonctions continues.C. R. Acad. Sci. Paris Sér. A-B 285 (1977), A1001–A1003. MR 0510870 |
| Reference:
|
[3] M. Errami and F. Russo: Covariation de convolution de martingales.C. R. Acad. Sci. Paris Sér. I Math. 326 (1998), 601–606. MR 1649341, 10.1016/S0764-4442(98)85014-3 |
| Reference:
|
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| Reference:
|
[5] D. Heath, A. Jarrow and A. Morton: Bond pricing and the term structure of interest rates: A new methodology for contingent claim valuation.Econometrica 60 (1992), 77–105. 10.2307/2951677 |
| Reference:
|
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| Reference:
|
[7] J.-P. Kahane: Baire’s category theorem and trigonometric series.J. Anal. Math. 80 (2000), 143–182. Zbl 0961.42001, MR 1771526, 10.1007/BF02791536 |
| Reference:
|
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| Reference:
|
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| . |
