Didier Piau
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Registered User
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May 15 |
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Continuous Differentiability under Expectation This is the classical problem of differentiation under the integral sign hence everything works fine under a domination condition. Not MO stuff. |
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May 10 |
accepted | Probability that one RV will exceed many others |
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May 10 |
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Markov transition probabilities and negative binomial distribution. "A realization of a Markov process generates a sequence of interval lengths between transition from one state to another." These lengths are always exponentially distributed, hence to get other lengths distributions one must leave the realm of Markov processes. If this is what you have in mind, you might want to explain in more details. |
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May 10 |
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Probability that one RV will exceed many others You are welcome. Is this the way you like to proceed: to get a full answer, then to write an incomplete one yourself and to accept it? |
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May 10 |
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Probability distribution for two-state system that depends on residence time I find a tad surprising that an answer restricted to the symmetric case $\kappa_+=\kappa_-$ is "what you were looking for" since the modifications needed to solve the general case are non trivial. For this reason, to ask whether my answer and the accepted one are the same seems rather moot and I do not feel much motivation to answer your last query. But since you seem happy with what you got, everything is perfect. (Unrelated: one cannot accept two answers.) |
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May 8 |
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Asymptotics of a function The main contribution is around $i=n/(4\log n)$, not around $i=n$. |
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May 8 |
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Asymptotics of a function Which context did you meet this beast in? |
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May 8 |
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Asymptotics of a function $f(n)=n^{n+o(n)}$. |
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May 8 |
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Probability distribution for two-state system that depends on residence time added 386 characters in body; added 10 characters in body |
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May 8 |
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Probability distribution for two-state system that depends on residence time added 543 characters in body |
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May 8 |
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Probability distribution for two-state system that depends on residence time If $p_+(\ ,t)$ and $p_-(\ ,t)$ are probability distributions, so is $p(\ ,t)$ as a barycenter of these. (But the question is about fixing $x$ once and for all and working on $p(x,\ )$ from $p_-(x,\ )$ and $p_+(x,\ )$, actually.) |
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May 8 |
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correlation for three variables? Hardly MO stuff, please try more adapted fora. |
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May 8 |
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compute the waiting time for a given pattern with Kac’s lemma As explained by others, Kac's lemma describes the mean return time to some word w starting from w. On the other hand, for the hitting time of w one starts from the empty word. Hence the hitting time is almost surely at least as large as the return time, likewise for their means. The mean hitting and return times coincide if and only if no terminal strict subword of w is an initial subword of w. For example, for w=HHHTT they coincide but for w=HTHTH they do not since HTH is both terminal and initial. |
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May 8 |
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Probability distribution for two-state system that depends on residence time deleted 2 characters in body |
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May 8 |
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Probability distribution for two-state system that depends on residence time Could you confirm or infirm the Edit? |
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May 8 |
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Probability distribution for two-state system that depends on residence time added 479 characters in body; added 103 characters in body; added 24 characters in body |
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May 7 |
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Probability distribution for two-state system that depends on residence time The answer is referring very precisely to the model you described. If you are interested in a different dynamics, please explain clearly what it is. Alternatively, describe what you think the problem with the derivation above is, avoiding vague terms such as "the fact that p±(x,t) evolves with time" (of course it "evolves with time", otherwise what would the argument $t$ be there for?). |
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May 7 |
answered | Probability distribution for two-state system that depends on residence time |
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May 6 |
answered | Probability that one RV will exceed many others |
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May 6 |
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Placing Bounds on Correlation/Covariance Through Correlation with an Intermediate Variable Thus, if $c_{1,2}=c_{1,3}=0.99$, then $2(0.99)^2-1\leqslant c_{2,3}\leqslant1$ (and every value inbetween can be realized). |
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May 6 |
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Closed form solution to an iterative equation. Standard comparison to the associated differential equation yields $y(n)=\Theta(n^b)$ with $b=1/(1-a)$ (and, with some more care, much more precise estimates) but this is not a research question. You might want to try math.stackexchange.com instead. |
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May 3 |
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Random graphs nonisomorphic to unit distance graphs @Benoît But the homework factor. |
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May 1 |
awarded | ● Nice Question |
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Apr 30 |
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Mathematicians whose works were criticized by contemporaries but became widely accepted later deleted 2 characters in body |
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Apr 29 |
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A sampling and learning question See en.wikipedia.org/wiki/Mode_%28statistics%29. |
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Apr 29 |
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A sampling and learning question Try the mode of the results $b$. |
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Apr 29 |
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Distribution of convex combination of i.i.d Gamma random variables I have also posted this question... on a site where some objections to the first inequality were raised. Any follow-up on these? |
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Apr 29 |
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Quadratic Variation and Distribution I fail to see a question here, "the relation between distribution of $X_n$ and the process $S_n$" can mean about anything, no? |
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Apr 29 |
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Intution behind conditional expectation when sigma algebra isn’t generated by a partition Apparently simultaneously crossposted at MSE. |
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Apr 22 |
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The first eigenvalue of a branching process matrix Conditionally on non-extinction. |
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Apr 22 |
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The first eigenvalue of a branching process matrix if it is larger than 1, then there are types that won't get extinct... is not accurate: rather, there is a positive probability that some types will not get extinct. |
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Apr 10 |
accepted | Integral of the product of Normal density and cdf |
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Apr 10 |
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Integral of the product of Normal density and cdf A faulty step is "At this point, given that" since when $B\to-\infty$, the product you consider goes to $\Phi(0)\phi(f)=\frac12\phi(f)\ne0$. |
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Apr 10 |
answered | Integral of the product of Normal density and cdf |
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Mar 26 |
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Is the Binomial Expectation of a Multivariate Convex Function Convex in the Vector p? @Hugh The function $h$ defined by $h(x_1,x_2)=(1-x_1)+(1-x_2)+1$ is linear hence there is no counterexample there. If you mean $h(x_1,x_2)=(1-x_1)(1-x_2)+1$, then this is Victor's example modulo an irrelevant affine part. |
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Mar 25 |
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Understanding Proof on paper “ is Pitmann Closeness a reasonable criterion" And you really expect people to go and check what (2.1), (2.2), (2.3) and (2.4) are? Voting to close. |
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Mar 25 |
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Minimum of exponential distributions Hardly MO stuff. Voting to close. |
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Mar 18 |
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Uniformly integrable sequence such that a.s. limit and conditional expectation do not commute edited body |
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Mar 18 |
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Uniformly integrable sequence such that a.s. limit and conditional expectation do not commute edited title |
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Mar 17 |
awarded | ● Scholar |
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Mar 17 |
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Compactness of sigma-algebra for the $L^1$ metrics @Rabee Thanks. What do you call "not compact in $L^1$"? Which part of Dunford and Schwartz? |
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Mar 17 |
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Compactness of sigma-algebra for the $L^1$ metrics @Julien Thanks for this answer. To which probability measures on [0,1], apart from the Lebesgue measure, does this apply? |
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Mar 17 |
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Ito formulae for stochastic processes with finite cubic, quartic … n-tic variation You are welcome. Always better to have an answer by the experts... Would you suggest that the OP reads Errami and Russo 2003 BEFORE these other, more recent, references, or not necessarily so? |
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Mar 17 |
asked | Compactness of sigma-algebra for the $L^1$ metrics |
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Mar 15 |
awarded | ● Yearling |
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Mar 13 |
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Ito formulae for stochastic processes with finite cubic, quartic … n-tic variation See ERRAMI M. and RUSSO F. (2003). n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes. Stochastic Process. Appl. 104 259–299. |
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Feb 15 |
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Convexity in $\{0,1\}^n$ added 6 characters in body; edited title; edited title |
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Jan 29 |
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Journals for undergraduates deleted 4 characters in body |
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Jan 29 |
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Journals for undergraduates deleted 1 characters in body |
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Jan 22 |
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Expectation of random matrix inverse added 5 characters in body; edited tags |
