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Janak
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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)$$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?

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.

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

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?

Source Link
Janak
  • 213
  • 1
  • 7

Defining a brownian bridge indexed by angle

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.

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