86 What is the importance of the infinitesimal generator of Brownian motion? 56 The $l^{\infty}$-norm is equal to the limit of the $l^{p}$-norms. 55 Angle bracket and sharp bracket for discontinuous processes 39 Density of first hitting time of Brownian motion with drift 36 Integral of Brownian motion is Gaussian?

### Reputation (109,272)

 -2 What does it mean to say a martingale is closed? +15 If a convex set $S \subseteq R^n$ contains no ray, can you show that it's bounded? +10 David Williams "Probability with Martingales" 4.12: Tail sigma algebras warning +10 Are the following Stopping Times?

### Questions (31)

 35 Collection: Results on stopping times for Brownian motion (with drift) 29 Martingale theory: Collection of examples and counterexamples 16 Existence of iid random variables 10 Weak generator of Feller semigroup 10 Conditions for the existence of a density with respect to Lebesgue measure

### Tags (246)

 4k probability-theory × 1264 1k martingales × 389 3k stochastic-processes × 849 960 probability × 400 2k brownian-motion × 535 792 real-analysis × 257 1k measure-theory × 532 713 stochastic-integrals × 235 1k stochastic-calculus × 416 679 convergence-divergence × 246

### Bookmarks (33)

 22 If $\int_{\mathbb R^2} \frac{\vert f(x)-f(y)\vert}{\vert x-y\vert^2}dxdy<+\infty$ then $f$ is a.e. constant 20 Is the set $\{ (X_n)_{n \in \mathbb{N}} \text{ has a nondecreasing subsequence} \}$ measurable? 18 Collection of standard facts about convergence of random variables 17 Does this random variable have a density? 15 Conditional expectation equals random variable almost sure