# Tagged Questions

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### Product of stochastically independent random variables

Let $X, Y, Z$ be three stochastically independent random variables that are quadratic integrable (quadratintegriertbar is the German term, I didn't find a exact translation). No which statements hold ...
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### is $(x-6)^2$ in $C_0^2$?

My math problem involves using a theorem that requires $f(x)=(x-6)^2$ to be in $C_0^2$. I'm trying to understand what $C_0^2$ means and how to check whether a function belongs to it. The course I'm ...
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### Expectation of stochastic differential equation

I have solved the nonlinear stochastic equation $dX_t=\frac{1}{2}a(a-1)X_t^{1-2/a}dt+aX_t^{1-1/a}dW_{t}$, by reducing it to a linear one (change of variables $Y_{t}=X_{t}^{1/a}$ and applying Ito ...
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Let B = (Bt)t¸0 be a standard Brownian motion started at zero, let $X_t$ be a non negative stochastic process solving: $dX_t=1/X_tdt+dB_t$ Compute $E[\sigma]$ when $\sigma=\inf \{ t\ge 0 : X_t= 1 ... 2answers 92 views ### Martingale Proofs I havent been able to find an analogous question and our textbook is lacking in good examples, so I could use a little help with this rather straight forward martingale problem: Let X=(Xn) be a ... 0answers 39 views ### is this solution correct about joint distribution? The question is if$x,y,z$are independent$x\sim\exp(\lambda), y\sim\exp(\mu), z\sim\exp(\gamma)$and define$u=\min(x,y), v=\min(y,z)$what is the probability$p(U>u,V>v)$. Consider the cases ... 1answer 65 views ### Advanced urn problem Imagine there are two urns — urn A and urn B. Urn A contains 3 blue balls and 7 red balls. Urn B contains 7 blue balls and 3 red balls. Balls are now randomly drawn from one of these urns where the ... 2answers 64 views ###$X_1,X_2,…$real independent random variables$\not\implies S_n = \frac{1}{n}(X_1+ \cdots + X_n)$are independent Is it possible to show the following Lemma: Given independent real random variables$(X_i)_{i\in \mathbb{N}}$, then$(S_n := \frac{1}{n}(X_1+\cdots + X_n))_{n \in \mathbb{N}}$are independent as ... 1answer 143 views ### Ito differential equation Define $$X_t := \left( \begin{matrix} \cos W_t \\ \sin W_t \end{matrix} \right).$$ where$W = \left( W_t,\mathcal F_t \right) _{t\ge0}$is a standard Wiener process. Find the Ito differential of X ... 2answers 30 views ### Algebraic problem for satisfying a given equation I'm trying to solve the following exercise: My backward equation looks like:$P_{i,j}'(t) = i\lambda P_{i+1,j}(t) - i\lambda P_{i,j}(t) $So i started with differentiating$P_{i,j}(t)$:${j-1 ...
Given a standardized normal variable $X\sim N\left(0,1\right)$, and constants $\kappa \in \left[0,1\right)$ and $\tau \in \mathbb{R}$, I want to sign the following expression: ...