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Martin Sleziak
Martin Sleziak
5:08 AM
1
Q: Unicoherence of the two-dimensional sphere

CarinaA connected space $X$ is said to be unicoherent if for any two closed connected subspaces $A$, $B$ such that $A\cup B = X$ then $A\cap B$ is connected. I came across an exercise which asks to show that $I=[0,1]$ is unicoherent, that $S^1$ is not, and to determine whether $S^2$ is unicoherent or n...

general-topology topology
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12 hours later…
Martin Sleziak
Martin Sleziak
5:43 PM
0
Q: Intuition for formula of variance of Brownian Motion conditioned on two endpoints

nullUserI am familiar with the following interpolation property of Brownian Motion (this is essentially a theorem about a Brownian Bridge): Theorem. Let $W$ be a standard Brownian Motion, and $0<t_1 < t < t_2$. Then the conditional distribution of $W_t$ given $W_{t_1}=x_1$ and $W_{t_2}=x_2$ is $N(\mu, \s...

probability-theory probability-distributions brownian-motion stochastic-analysis brownian-bridge
Brownian bridge
A Brownian bridge is a continuous-time stochastic process B(t) whose probability distribution is the conditional probability distribution of a Wiener process W(t) (a mathematical model of Brownian motion) subject to the condition (when standardized) that W(T) = 0, so that the process is pinned at the origin at both t=0 and t=T. More precisely: B t := ( W t ∣ W T =...
 

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