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Results tagged with pr.probability
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user 70478
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Accepted
A note on Doob's theorem
It is true. Here is an elementary proof, without relying on the martingale convergence theorem.
Let us first consider the case when $f:[0,1]\to \mathbb{R}$ is continuous. If $I\subseteq [0,1]$ is an i …
- 179
1
vote
Quadratic variation and predictable quadratic variation for martingales
It is true that $\langle M\rangle^n_1 \to \langle M\rangle_1$ in $L^1$ when $M$ is a continuous square-integrable martingale.
Indeed, $M^2$ is then a submartingale of class D and so, since
$$E[(M_{t_ …
- 179
4
votes
Accepted
Examples of a continuous martingale with $E[\sup\limits_{0\leq s\leq t} |M_s|]=\infty$?
There exist indeed a uniformly integrable martingale $X$ such that $\sup_{t} |X_t|$ is not integrable. Here a list of several examples:
A simple example in discrete time can be found here http://www …
- 179