Karhunen–Loève expansion for a generalization of Wiener bridge
We derive a Karhunen--Lo\`{e}ve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u) dB_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2 du =1$. This proce...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2018
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| Sorozat: | LITHUANIAN MATHEMATICAL JOURNAL
58 No. 4 |
| Tárgyszavak: | |
| doi: | 10.1007/s10986-018-9413-4 |
| mtmt: | 30344036 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/39626 |
| Tartalmi kivonat: | We derive a Karhunen--Lo\`{e}ve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u) dB_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2 du =1$. This process is an important limit process in the theory of goodness-of-fit tests.We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$. |
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| Terjedelem/Fizikai jellemzők: | 341-359 |
| ISSN: | 0363-1672 |