815 reputation
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bio website emanuelenatale.isnphard.com
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visits member for 3 years, 6 months
seen Jul 4 at 15:48

Jul
2
awarded  Curious
Feb
23
awarded  Yearling
Jul
17
awarded  Notable Question
Jul
11
comment What is meant by “constant” in the optional stopping theorem?
Is the optional stopping theorem still true with a definition of stopping time that allows it to be infinite? I think no: let the random walk stop moving as it reaches $m$ or $-m$, but define the stopping time to be the time it reaches $m$; this stopping time is infinite but if we could use part (c) we got a contradiction.
Jul
10
comment What is meant by “constant” in the optional stopping theorem?
Thank you! I did not encounter that definition of stopping time before (I'm in the "some cases" of the Wikipedia definition en.wikipedia.org/wiki/Stopping_time#Definition).
Jul
10
accepted What is meant by “constant” in the optional stopping theorem?
Jul
10
asked What is meant by “constant” in the optional stopping theorem?
Apr
22
awarded  Tumbleweed
Apr
15
asked Some questions about a “relaxed” invariant probability problem $|\mu(P-I)|\leq \epsilon$
Feb
23
awarded  Yearling
Jan
29
accepted How to formally write a property of a specific coloring of a graph.
Jan
28
asked How to formally write a property of a specific coloring of a graph.
Dec
2
awarded  Analytical
Dec
2
accepted On the meaning of the equal sign when used to define the event of a r.v. taking some value.
Dec
2
comment On the meaning of the equal sign when used to define the event of a r.v. taking some value.
@MichaelHardy sorry, I rewrote $\{\omega : X(\omega)=k-Y\}$ without noticing to become redundant.
Dec
2
asked On the meaning of the equal sign when used to define the event of a r.v. taking some value.
Nov
30
comment Estimate the density function of a distribution based on binomial distributions.
It seems to me that the problem could be stated within a simpler equivalent scenario: we toss $K$ red coins and $I$ blue coins that follow a Bernoulli$(\frac{c}{n})$ and ask what is the probability that the red heads are more than the blue ones. Then, if the two numbers are called $X$ and $Y$, I want the probability that $X-Y$ is positive. I've tried to get the density using characteristic functions but I'm not able to calculate the inverse Fourier Transform (maybe it's a silly approach 'cause give a worse problem than estimating the formula we start with). Do you have further suggestions?
Nov
30
awarded  Benefactor
Nov
30
accepted Estimate the density function of a distribution based on binomial distributions.
Nov
30
comment Estimate the density function of a distribution based on binomial distributions.
I've already analysed the case where a node gets a certain colour iff it is the only colour it sees, that is a ``stronger'' case you use to give bounds. I was interested in something finer (a better approximation of the given formula), however you're question is the only that gives a valid approximation and the bounty is expiring, than I thank you very much for your effort.