A Discrete Construction for Gaussian Markov Processes
| dc.creator | Taillefumier, Thibaud | |
| dc.date | 2008-05-01 | |
| dc.date | 2008-06-10 | |
| dc.date.accessioned | 2026-07-07T09:43:12Z | |
| dc.date.available | 2026-07-07T09:43:12Z | |
| dc.description | In the Lévy construction of Brownian motion, a Haar-derived basis of functions is used to form a finite-dimensional process $W^{N}$ and to define the Wiener process as the almost sure path-wise limit of $W^{N}$ when $N$ tends to infinity. We generalize such a construction to the class of centered Gaussian Markov processes $X$ which can be written $X_{t} = g(t) \cdot \int_{0}^{t} f(t) dW_{t}$ with $f$ and $g$ being continuous functions. We build the finite-dimensional process $X^{N}$ so that it gives an exact representation of the conditional expectation of $X$ with respect to the filtration generated by ${\lbrace X_{k/2^{N}}\rbrace}$ for $0 \leq k \leq 2^{N}$. Moreover, we prove that the process $X^{N}$ converges in distribution toward $X$. | |
| dc.identifier | https://arxiv.org/abs/0805.0048 | |
| dc.identifier | http://arxiv.org/abs/0805.0048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162469 | |
| dc.subject | Probability | |
| dc.title | A Discrete Construction for Gaussian Markov Processes | |
| dc.type | text |