User adrien - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T15:51:13Z http://mathoverflow.net/feeds/user/26018 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108895/total-variation-distance-between-a-poisson-and-a-distribution-with-known-mean-var/108900#108900 Answer by Adrien for Total variation distance between a Poisson and a distribution with known mean/variance Adrien 2012-10-05T09:05:21Z 2012-10-05T09:05:21Z <p>Maybe you could use <a href="http://en.wikipedia.org/wiki/Pinsker%27s_inequality" rel="nofollow">Pinsker's Inequality</a> to get an upper bound on the quantity you're interested in ? There are lot of results about finding distributions minimizing the Kullback-Leibler divergence (this problem is also sometimes called Information Projection). Though not sure this is useful since you seem more interested in a lower bound...</p> http://mathoverflow.net/questions/107364/the-probability-distribution-of-random-variable-of-random-variable/107366#107366 Answer by Adrien for The Probability distribution of Random variable of Random variable Adrien 2012-09-17T08:46:29Z 2012-09-17T08:46:29Z <p>$Y(X)$ doesn't mean anything. You can't define the composition of random variables. What you can do is compose a random variable $X$ by a measurable function $f$ (provided the $\sigma$ algebras are the same) : $f(X)$.</p> <p>So in your example, there are two different objects, measurable functions and random variables :</p> <p>-the measurable functions $f$ from $(A,\sigma_A)$ to $(B,\sigma_B)$ and $g$ from $(B,\sigma_B)$ to $(C,\sigma_C)$. Since B uses the same $\sigma$-algebra, the function $g \circ f$ is measurable from $(A,\sigma_A)$ to $(C,\sigma_C)$.</p> <p>-the random variable when you add a probability distribution to the measurable spaces. So if you add $P_A$ to $(A,\sigma_A)$, the measurable function $f$ from $(A,\sigma_A)$ to $(B,\sigma_B)$ induces a random variable we can write $X$. Now since we also have a measurable function $g \circ f$ from $(A,\sigma_A)$ to $(C,\sigma_C)$, it also induces another random variable that we can write $X'$ or more usually $g(X)$. And if you add $P_B$ to $(B,\sigma_B)$, function $g$ induces a random variable we'll write $Y$.</p> <p>But the composition $Y(X)$ doesn't makes any sense.</p> http://mathoverflow.net/questions/107117/what-is-the-name-for-a-non-normalized-distribution/107123#107123 Answer by Adrien for What is the name for a non-normalized distribution? Adrien 2012-09-13T20:20:15Z 2012-09-13T20:20:15Z <p>Measures ? They are also more restrictive subsets of measure like finite measures or $\sigma$-finite measures.</p> http://mathoverflow.net/questions/107364/the-probability-distribution-of-random-variable-of-random-variable/107366#107366 Comment by Adrien Adrien 2012-09-19T08:36:43Z 2012-09-19T08:36:43Z Well, you could define a random variable this way and write it $X$ or $Y$, but this is already defined as a measurable function, and it is usually written with small letters life $f$ or $g$ :) So if you want to be understood, you should speak of $g \circ f$ (measurable function), or $g(X)$ for the random variable, but not $Y(X)$.