# Didier Piau

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## Registered User

 Name Didier Piau Member for 3 years Seen 11 hours ago Website Location Age
 May15 comment Continuous Differentiability under ExpectationThis is the classical problem of differentiation under the integral sign hence everything works fine under a domination condition. Not MO stuff. May10 accepted Probability that one RV will exceed many others May10 comment 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. May10 comment Probability that one RV will exceed many othersYou 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? May10 comment Probability distribution for two-state system that depends on residence timeI 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.) May8 comment Asymptotics of a functionThe main contribution is around $i=n/(4\log n)$, not around $i=n$. May8 comment Asymptotics of a functionWhich context did you meet this beast in? May8 comment Asymptotics of a function$f(n)=n^{n+o(n)}$. May8 revised Probability distribution for two-state system that depends on residence timeadded 386 characters in body; added 10 characters in body May8 revised Probability distribution for two-state system that depends on residence timeadded 543 characters in body May8 comment Probability distribution for two-state system that depends on residence timeIf $p_+(\ ,t)$ 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.) May8 comment correlation for three variables?Hardly MO stuff, please try more adapted fora. May8 comment compute the waiting time for a given pattern with Kac’s lemmaAs 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. May8 revised Probability distribution for two-state system that depends on residence timedeleted 2 characters in body May8 comment Probability distribution for two-state system that depends on residence timeCould you confirm or infirm the Edit? May8 revised Probability distribution for two-state system that depends on residence timeadded 479 characters in body; added 103 characters in body; added 24 characters in body May7 comment Probability distribution for two-state system that depends on residence timeThe 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?). May7 answered Probability distribution for two-state system that depends on residence time May6 answered Probability that one RV will exceed many others May6 comment Placing Bounds on Correlation/Covariance Through Correlation with an Intermediate VariableThus, 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). May6 comment 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. May3 comment Random graphs nonisomorphic to unit distance graphs@Benoît But the homework factor. May1 awarded ● Nice Question Apr30 revised Mathematicians whose works were criticized by contemporaries but became widely accepted laterdeleted 2 characters in body Apr29 comment A sampling and learning question Apr29 comment A sampling and learning questionTry the mode of the results $b$. Apr29 comment Distribution of convex combination of i.i.d Gamma random variablesI have also posted this question... on a site where some objections to the first inequality were raised. Any follow-up on these? Apr29 comment Quadratic Variation and DistributionI fail to see a question here, "the relation between distribution of $X_n$ and the process $S_n$" can mean about anything, no? Apr29 comment Intution behind conditional expectation when sigma algebra isn’t generated by a partitionApparently simultaneously crossposted at MSE. Apr22 comment The first eigenvalue of a branching process matrixConditionally on non-extinction. Apr22 comment The first eigenvalue of a branching process matrixif 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. Apr10 accepted Integral of the product of Normal density and cdf Apr10 comment 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 $\Phi(0)\phi(f)=\frac12\phi(f)\ne0$. Apr10 answered Integral of the product of Normal density and cdf Mar26 comment 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. Mar25 comment 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. Mar25 comment Minimum of exponential distributionsHardly MO stuff. Voting to close. Mar18 revised Uniformly integrable sequence such that a.s. limit and conditional expectation do not commuteedited body Mar18 revised Uniformly integrable sequence such that a.s. limit and conditional expectation do not commuteedited title Mar17 awarded ● Scholar Mar17 comment 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? Mar17 comment 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? Mar17 comment Ito formulae for stochastic processes with finite cubic, quartic … n-tic variationYou 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? Mar17 asked Compactness of sigma-algebra for the $L^1$ metrics Mar15 awarded ● Yearling Mar13 comment Ito formulae for stochastic processes with finite cubic, quartic … n-tic variationSee 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. Feb15 revised Convexity in $\{0,1\}^n$added 6 characters in body; edited title; edited title Jan29 revised Journals for undergraduatesdeleted 4 characters in body Jan29 revised Journals for undergraduatesdeleted 1 characters in body Jan22 revised Expectation of random matrix inverseadded 5 characters in body; edited tags