# Questions tagged [martingale]

In probability theory, a martingale is a model of a fair game where knowledge of past events never helps predict the mean of the future winnings and only the current event matters.

45 questions
Filter by
Sorted by
Tagged with
1k views

856 views

### Martingale Difference & Conditional Heteroskedasticity

I was reading this passage in a book and I am confused about the last line. As far as I understand, the white noise process does not allow for conditional heteroskedasticity due to its i.i.d. property....
97 views

### Prove $Z_n = X_n1_{n \le T} + Y_n1_{n+1\ge T}$ is a martingale

Given a filtered probability space $(\Omega, \mathscr F, \{\mathscr F_n\}, \mathbb P)$, let $X = (X_n)_{n \in \mathbb N}$ and $Y = (Y_n)_{n \in \mathbb N}$ be $(\{\mathscr F_n\}, \mathbb P)-$...
127 views

### Upper bound for randomly weighted sum of independent random variables

I have a sequence of independent random variables {$\epsilon_j$} with mean 0. I also have another sequence of Bernoulli random variables $\delta_1, \delta_2,\dots$ which are dependent on the previous ...
24 views

### 1_event set notation

I do not understand the notation as given here: The source for the image is page 17 in this paper after equation 18. I understand the first subset notation but what does 1_\e_t mean?
2k views

### Why white noise process and IID process are considered martingale [closed]

Can anyone explain to me why A white noise process (εt) and An IID process (εt) are martingales?
52 views

### $M_t$ Local Martingale if and only if satisfies $\frac{\partial f}{\partial t}+\frac{1}{2}\frac{\partial^2 f}{\partial x^2}=0$ proof?

I was reading the wikipedia article on local martingales and it states the following theorem Let $W_t$ be standard Brownian motion and let $f:[0,\infty)\times\mathbb{R}\rightarrow\mathbb{R}$ such ...
18 views

### An inequality about expectation [duplicate]

If $X_n$ is a martingales with $sup E|X_n|^p<\infty$ where $p>1$, How can show that $$E^p|X_n|\leq E |X_n|^p$$
1k views