Nicolas Essis-Breton
Reputation
1,836
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Next privilege 2,000 Rep.
 Feb 1 accepted Set of continuous function defined on some segment $[0,a]$: triangle inequality Jan 18 accepted Levy process : $E\left[\exp\left(\theta^*X_\tau -\Psi(\theta^*)\tau\right)1_{\{\tau < \infty\}}\right] = e^{\theta^*x}P\left( \tau < \infty \right)$ Jan 16 accepted Distribution of the number of children needed so that at least both a girl and a boy are born Jan 15 accepted Show the Fourier transform is continuous in the Schwartz space $\mathcal S(\Bbb R)$ Jan 15 accepted Give an example: $X, Y$ metric space, $X$ not compact, there is no $V$ for which $f^{-1}(V) \subset U$ Dec 29 accepted Compound Poisson process: calculate $E\left( \sum_{k=1}^{N_t}X_k e^{t-T_k} \right)$, $X_k$ i.i.d., $T_k$ arrival time Dec 29 accepted True or False: $f$ analytic in the right plane, continuous on the boundary, $|f| \le 1$ on the boundary, then $|f| \le 1$ Dec 29 accepted $T,U$ self-adjoint, $U$ positive definite, then $TU$ has only real eigenvalues Dec 27 accepted If n people randomly pick one hat out of n hats, why is the probability of a match $1/n$? What about order of previous hats? Dec 27 accepted Show $\int_0^1 f(x) dx \int_0^1 \ln f(x) dx \le \int_0^1 f(x) \ln f(x) dx$, when $f \ge 1$ Dec 26 accepted Show $\ln x \le x \ln x, x > 0$ Dec 26 accepted Show $\exists f \ni f(x)^5+f(x)^4+f(x)^3+f(x)^2+6f(x)=x$ Dec 18 accepted Dirichlet Problem: Uniqueness of solution Nov 20 accepted Dirichlet problem: Obtaining the harmonic measure through Riesz representation theorem Nov 19 accepted Dirichlet problem: Is the Poisson Integral always a solution? Nov 13 accepted Quadratic variation of $X_t=\int_0^t B_s \, ds$ Nov 13 accepted Condition for existence of a stochastic differential equation Nov 13 accepted Find the Hardy-Littlewood maximal function of $\chi_{[-1,1]}$ on $\Bbb R$ Nov 12 accepted Show the convolution of a $C_c^\infty (\Bbb R^n)$ function with a $L^p(\Bbb R^n)$ function is in $C^\infty(\Bbb R^n)$, $1\le p\le\infty$ Nov 9 accepted Show a Schwartz function vanish at infinity