Activity for Alex de Ruijter‭

Type	On...	Excerpt	Status	Date
Edit	Post #293197	Initial revision	—	about 2 months ago
Answer	—	A: High-Probability Lower Bound for Sums of Conditional Probabilities in IID Sequences on the Unit Sphere I've found a way to generalize the proof. So we know $x\in \mathbb S^{d-1}$. Now that implies that there exists a threshold $\alpha>0$ such that $\sum{i=1}^d \mathbf{1}\{|xi|>\alpha\}\geq 1$ where $\mathbf{1}\{A\}$ is an indicator-function. We know that this $\alpha$ exists. It's upper-bound ... (more)	—	about 2 months ago
Edit	Post #293143	Initial revision	—	about 2 months ago
Answer	—	A: High-Probability Lower Bound for Sums of Conditional Probabilities in IID Sequences on the Unit Sphere So for $(d=2)$ this is my solution; First fix some $i\geq 1$ and let us investigate $$ \mathbb P \left\\{|u{i:i-1}\\, x| >\alpha \mid \mathcal F{i-1} \right\\} $$ for some vector $x = [x1, x2]^T$ on the unit circle. Then we have four cases. 1. $u{i-1}=1$ and $|x2|>\alpha$: Then if $ui=... (more)	—	about 2 months ago
Edit	Post #293142	Initial revision	—	about 2 months ago
Question	—	High-Probability Lower Bound for Sums of Conditional Probabilities in IID Sequences on the Unit Sphere Let $(\Omega, \mathcal F, \mathbb P)$ be a filtered probability space. Let $\{u\}{i=1}^\infty$ be a sequence of i.i.d. RV's, $ui\sim Ber(\frac{1}{2})\,\forall i\in\mathbb N$, where we define $ui = 0 \,\forall i \leq 0$. Let $\mathcal Fi$ be the natural filtration $\sigma(u1, u2, \ldots, ui)$, with $... (more)	—	about 2 months ago