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Results tagged with stochastic-processes
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user 62190
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
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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 (centroid …
- 213
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Sum of two parts of a continuous stochastic process
Let $X$ be a centered continuous stochastic process which is square integrable on $[0,2]\times \Omega$ and the basis of $L^2(0,2)$ is $\{e_i\}$. By using Karhunen-Leove Theorem one can write for all $ …
- 213
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Weighted sum of standard Brownian bridges
Let $\{B_j\}_{j=1}^k$ be a sequence of Brownian bridges.
Let us consider $$X(t)=\sum_{j=1}^m w_j(t)B_j(t),$$ where $w_j$ are positive weight functions.
Then what can we say about (distribution or may …
- 213
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Defining density of a random function using Radon-Nikodym Theorem
Let $(\Omega,\mathbb{F},P)$ be a probability space and $E$ be an infinite dimensional Banach space and $\mathbb{B}$ be the $\sigma$-algebra of Borel subset of $E$.
Let $X$ be random function defined …
- 213