# Tagged Questions

44 views

### How to prove $(X_{n})_{n\in \mathbb N}$ and $(Y_{n})_{n\in \mathbb N}$ are supermartingale and $(Y_{n})_{n\in \mathbb N}$ is convergence to -7

Let $p \in [0 , \frac{1}{2}]$ and $\eta_{i}$ be i.i.d random variables and $P(\eta_{i}=1)=p$ and $P(\eta_{i}=-1)=1-p$ and $\mathcal F_{n}=\sigma(\eta_{1},\cdots,\eta_{n})$ and ...
62 views

### If $X_{n+1}$ is a martingale subject to $Y_0,\ldots,Y_n$, then is it a martingale with respect to $Y_0^2,\ldots,Y_n^2$?

I don't have a very solid foundation in measure theory, and this always seems a bit confusing to me so I would appreciate any help. We are given $E \left( X_{n+1} | Y_0,\ldots,Y_n \right) = X_n.$ ...
52 views

### Bayesian random walk: updating on samples from posterior

Suppose that, at first, I am trying to estimate the mean and standard deviation of some data that I assume to be normally distributed. My prior is gaussian with mean $\mu_0$ and variance $\sigma^2_0$. ...
Consider two Wiener processes: \begin{aligned} X_a &\sim\mathcal N(0,a) \\ X_{a-b} &\sim\mathcal N(0,a-b) \end{aligned} How do I show that: $$X_a - X_{a-b} \sim\mathcal N(.,.)$$ That ...