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Mathematics
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Kurt.W.X
  • Member for 4 years, 3 months
  • Last seen more than 2 years ago
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8
If $X_n \to X $ in probability then $f(X_n) \to f(X)$ in probability for a Borel function $f$
Feb 25, 2021
7
$E[(Y_1-f(x))^2] \leq E[(Y_2-Y_1)^2]$
Oct 21, 2021
6
Proof of the identity $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$ for $\alpha\in (0,2)$.
Aug 28, 2020
5
If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $\lim_{k \to \infty} E[X\mid\mathcal{F}_k]=E[X\mid\mathcal{W}]$ a.s?
Aug 9, 2021
5
$\exists c \in\mathbb{R}_+^*,\forall p,r\in \mathbb{R}_+,E[|X_{p+r}-X_r||\mathcal{F}_r] \leq c$ implies the optional stopping theorem
Aug 5, 2021
5
If $\lim_k \mathcal{F}_k=\mathcal{W}$ then $E[X\mid\mathcal{F}_k]$ converges to $E[X\mid\mathcal{W}]$
Jun 24, 2021
5
Necessary and sufficient condition for weak convergence and convergence of density
May 24, 2020
4
Law of the iterated logarithm of a Brownian motion in $\mathbb{R}^q$
Mar 14, 2022
4
$\lim\limits_nx_n=0,\forall n \in \mathbb{N},\phi_X(x_n)=e^{-\sigma^2x^2_n} \implies \forall x \in \mathbb{R}, \phi_X(x)=e^{-x^2\sigma^2} $
Mar 3, 2021
4
Strong law of large numbers without independence
Jun 24, 2020