6,042 reputation
428
bio website twitter.com/SimeonLePoisson
location France
age 25
visits member for 1 year, 4 months
seen 12 hours ago

I am a Ph.D student working in the field of Probability Theory.


Apr
14
answered Inequality involves complex numbers
Mar
12
comment A basic question on distribution function and stieljes integral
You can prove that if $X$ and $Y$ are independent, the first integral is $\Pr(Y \leq X)$ and the second one is $\Pr(X \leq Y)$.
Jan
21
awarded  Nice Answer
Jan
14
reviewed Approve suggested edit on L'Hôpital's rule for $\mathbb R ^n \to \mathbb R $ functions.
Jan
12
comment Showing convergence of a series
@Leitingok: By ($\ast$) and the triangular inequality, $|a_{n+1}| \leq |1-\frac{2}{n+1}||a_n| + |\epsilon| = (1-\frac{2}{n+1})|a_n| + |\epsilon_n|$ because $(1-\frac{2}{n+1}) \geq 0$.
Jan
11
reviewed Approve suggested edit on What is the sum of this series? Dirichlet $L$-Function
Jan
10
comment Big-$O$ notation definition.
To emphasize the lack of uniformity in R.
Jan
10
comment Integration, Lebesgue and counting measure
These integrals reduce to $m(\{y\})$ and $\omega(\{x\})$. I let you finish.
Jan
10
comment Big-$O$ notation definition.
For all $R < 2$, there exists a constant $C_R$ such that [...] Maybe $C_R = |R|$ or maybe $C_R = \pi+\sqrt{2}$ or maybe $C_R = e^{e^{R^2}}$... the $O_R(x)$ doesn't say.
Jan
10
comment Big-$O$ notation definition.
@martin: $C_R$ is a positive real number.
Jan
10
awarded  Custodian
Jan
10
reviewed No Action Needed Complete course of self-study
Jan
10
reviewed Leave Closed Find $x, y$ such that $\left | \frac ab -\frac xy \right |$ is minimal
Jan
10
reviewed Close Two of the zeros of the polynomial $f(x)=x^3 + ax^2 + bx + c$ are opposite numbers. (a,b,c are real).
Jan
10
reviewed Close Numerical methods for stochastic differential equations
Jan
10
reviewed Leave Open Which methods different than the natural $\lim_{n\to\infty}\frac{|\cos{1}|+|\cos{2}|+|\cos{3}|+\cdots+|\cos{n}|}{n}$
Jan
10
revised Big-$O$ notation definition.
added 141 characters in body
Jan
10
answered Big-$O$ notation definition.
Jan
8
comment Prove that $\lim_{n\to\infty}\left[1-\prod_{i=1}^{n} (1-\frac{a}{i} )\right]= 1$.
Huh, is it $\prod \frac{a}{i}$ or $\prod (1-\frac{a}{i})$?
Jan
8
reviewed Reviewed Evaluate $\int_0^1dx \int_0^1\frac{x^2-y^2}{(x^2+y^2)^2}dy$