Boby's user avatar
Boby's user avatar
Boby's user avatar
Boby
  • Member for 9 years
  • Last seen this week
  • Beijing, China
12 votes
2 answers
272 views

Show that $f(t)=\sum_{i=1}^n a_i e^{-(x_i-t)^2}-c$ has at most $2n$ zeros

7 votes
3 answers
271 views

Solve $\inf_{ X: |X| \le a \text{ a.s.}} E \left[ \frac{1}{1+(X-X^\prime)^2} \right] $

6 votes
2 answers
2k views

Bounds on the number of zeros of real analytic functions

6 votes
1 answer
315 views

Show that $M_X(t) = 2 E \left[ e^{tX} \Phi( aX-t) \right], \forall t \in \mathbb{R}$ iff $X$ is Gaussian

4 votes
0 answers
1k views

Show that $\mathbb{P}[ a V\le Z| V+Z]=\mathbb{P}[aV \ge Z| V+Z] \text{ a.s.} $ iff $V=\frac{1}{\sqrt{a}}Z'$ where $Z'$ is standard normal

3 votes
2 answers
413 views

How to solve the following $0= \int_{-\infty}^\infty e^{-\frac{(bt+\omega)^2}{2}} f(t+\omega) \frac{1}{i t} dt, \forall \omega \in \mathbb{R}$

3 votes
1 answer
116 views

Best approximation of normal with $m$ atoms in Kolmogorov-Smirnov distance

3 votes
1 answer
181 views

Generalization(s) of variation diminishing property to multivariate case

3 votes
1 answer
620 views

Extreme points of set of probability measures $\mathcal{P}= \{F: \int_{\mathbb{R}} |x|^k dF(x)=c \}$

2 votes
2 answers
593 views

An alternative proof of Bayesian Cramer-Rao

2 votes
0 answers
149 views

Sufficient condition for a solution to Hamburger moment problem

2 votes
1 answer
309 views

Questions about Levy measure in the canonical representation of infinitely divisible distributions

2 votes
1 answer
63 views

Maximum Number of modes of $V=U+Z$ where $Z$ standard normal and $|U|\le a$

2 votes
1 answer
142 views

Jensen's Formula for Arbitrary Neighborhoods

2 votes
1 answer
388 views

Bounds on cumulants in terms of moments

2 votes
1 answer
595 views

Radius of convergence of cumulant generating function

2 votes
1 answer
437 views

Extreme points of an intersection of convex set with countably many linear spaces

2 votes
1 answer
164 views

If $Z$ is standard normal and $f$ is analytic. Is $g(t)= E[ f(Z-t)]$ analytic?

1 vote
1 answer
181 views

Sufficient condition such that the set of zeros of an analytic function $f:\mathbb{R}^n \to \mathbb{R}$ contains only isolated points

1 vote
1 answer
151 views

Uniqueness of Fourier–Stieltjes transform for finite complex valued measures

1 vote
0 answers
144 views

Maximizing variance of bounded random variable through convex optimization

1 vote
0 answers
46 views

Example/counterexample of distribution $P$ such that $D(P\parallel Q) <\infty$ where $Q$ is Gaussian, but $E_P[X^2]=\infty$

1 vote
0 answers
436 views

Laplace transform of a random variable: Inversion formula from an interval

1 vote
1 answer
92 views

Proximity in terms of characteristic functions for $n$-dimensional distributions

1 vote
1 answer
395 views

Zeros of Multivariate Complex Functions [need reference]

1 vote
0 answers
330 views

Bounds on the distance between probability distributions in terms characteristic functions

1 vote
1 answer
259 views

Maximizing linear function (not necessarily continuous) over a compact, closed and convex domain

1 vote
1 answer
592 views

Extreme Points of a set of distributions with moment and/or support constraint

0 votes
0 answers
122 views

Does Hartogs's Theorem for complex-analytic functions hold for real-analytic functions? [duplicate]

0 votes
0 answers
69 views

Looking for example of integral transformations that preserve number of zeros