Showing that $\int^{t}_{0}B^{2}_{s}dB_{s}=\frac{1}{3}B^{3}_{t} - \int^{t}_{0}B_{s}ds$, without Ito formula
87149
Prove directly from the definition of the Ito's integral
113141
Prove that $\lim_{n \to \infty}\bigg[\int_0^1f(t)^n \text{dt}\bigg]^{1/n}=M$
141029
Questions regarding proof of probability integral transform
54244
Understanding the Proof of L'Hopital's Rule
99165
How to prove that for Brownian motion in $(a, b)$ $\mathbb{E}^x[\min(H_a, H_b)] = (x-a)(b-x)$?
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
149320
Proving an integral formula containing the Poisson kernel
154185
Evaluate $\iiint_{[0,1]^3}\frac{dx\,dy\,dz}{(1+x^2+y^2+z^2)^2}$
85311
Proving that $e^{\pi}-{\pi}^e\lt 1$ without using a calculator
142821
Why?$\int_0^1\int_{u(t)}^{u(t)+w(t)} f(t,v(t)) dv dt = \int_0^1 f(t,u(t)+\theta w(t))w(t) dt; ~~\theta\in[0,1] $
104853
Proving that $\lim\limits_{n\to\infty}n\left( \int_0^1 f(t)\, dt -\frac1n\sum_{k=0}^{n-1}f\left(\frac k n\right) \right)=\frac{f(1)-f(0)}{2}$
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
40019
Showing that $\gamma = -\int_0^{\infty} e^{-t} \log t \,dt$, where $\gamma$ is the Euler-Mascheroni constant.
144146
find a $\int_{x}^{g(x)} f(t)\,dt = 1$
35025
Solution to the linear SDE $dX_t = \alpha X_t \, dt + \sqrt{2} dB_t$ using Itô calculus
44416
Ito integral property
141286
When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?