# Tagged Questions

32 views

### How to prove the inequality using Jensen's inequlaity?

How to prove the above inequality? I am learning probability by myself and it has been confusing me for days. Thanks!
21 views

### How to prove the above expectation inequality?

If $\mathbb{E}[|X|^k]<\infty$ then for $0<j<k$, $\mathbb{E}[|X|^j]<\infty$, and furthermore $\mathbb{E}[|X|^j]\leq(\mathbb{E}[|X|^k])^{j/k}.$ How to prove the above expectation ...
11 views

69 views

66 views

146 views

### A counter example of Brownian Motion

Here is an example in my textbook to illustrate why we need the continuous sample path in the definition of Brownian motion. Let $(B_t)$ be a Brownian motion and $U$ be a uniform random variable on ...
23 views

### Filtration from a Brownian Motion

The textbook I am reading defines the filtration induced from a Brownian Motion as follows. Let $\{B(t): t \geq 0\}$ be a Brownian Motion defined on some probability space, then we can define a ...
Consider a homogeneous Markov chain $\{X_n\}_{n\in\mathbb N}$ with a countable (but not necessarily finite) state space $S$. Suppose that there exists a limit distribution $\pi$, namely: ...