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Results tagged with stochastic-processes
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user 7949
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
4
votes
Accepted
Residency time of a spherical Brownian particle in a cylindrical container with another sphe...
You can use the Feynman-Kac formula to get the Moment Generating Function of the time it takes the particle to leave.
I will consider the case where you fix $P_1$ and let $P_2$ move. Whatever the ge …
- 599
2
votes
Properties of the Euler Discretization of a diffusion
What you call the Euler discretization is sometimes called the Euler-Maruyama discretization. There is a lot of literature about its convergence properties. One place to look is the classic book by Kl …
- 599
3
votes
How long does it take a Brownian particle to achieve a uniform probability distribution acro...
Let $\rho(t,x)$ be the probability that the particle is at location $x$ at time $t$. $\rho$ satisfies the equation $\rho_t = \rho_{xx}$, with $\rho(0,x)=\delta(x-x_0)$ where $x_0$ is the starting pos …
- 599