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Results tagged with stochastic-processes
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user 520778
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
3
votes
1
answer
271
views
Laplace transform of Brownian motion functional
Let $(B_r,r\geq 0)$ be a standard Brownian motion on $\mathbb{R}$ started at $0$. I am interested in the quantity
$$g(s,t) = \mathbb{E}_0\left[ \exp \left(- \beta \int_s^t \left\vert \frac{B_r}{r}\rig …
- 228
0
votes
Accepted
Laplace transform of Brownian motion functional
Thanks to the reference of @Thomas Kojar, I now have a solution. The method using the Hadamard factorisation in https://www.webpages.uidaho.edu/~fuchang/res/EJP.pdf (Gao, Hannig, Lee, Torcaso; EJP 200 …
- 228
6
votes
1
answer
124
views
Coupling/Ordering of Brownian bridges
Suppose I have two 1D Brownian bridges $(B^{(1)}_t,t\in [0,1]),(B^{(2)}_t,t\in [0,1])$, one from $0$ to $0$ and one from $x$ to $y$ where $x,y \geq 0$. Is there a neat way to show that there exists a …
- 228