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I have a random closed curve of the form $(\theta,r_\theta)$, where $\theta\in [0,2\pi]$, is the counter clockwise angle from the x-axis and $r_\theta$ is the radial distance from the origin (centroid).

For example:

enter image description here

Is it possible to define a stochastic process $r=\{r_\theta: \theta \in [0,2\pi]\}$ as a Brownian bridge?

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I should have left this as a comment but since I don't have enough points, I have to leave it as a reply (even if it's not).

You cannot define $(r_\theta)$ as a brownian bridge because $r\geq 0,\, a.s.$ and if $r$ were a Gaussian process $P(\exists \theta \in[0,\pi]\,|\, r_\theta<0) >0$. You might check a Bessel bridge since the radial part of a BM is a Bessel process.

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  • $\begingroup$ Thank you..I missed that points (Gaussian part). Thanks for the suggestion (Bessel process). $\endgroup$
    – Janak
    Commented Mar 30, 2015 at 16:18

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