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saz's user avatar
saz
  • Member for 10 years, 2 months
  • Last seen more than a month ago
  • Germany
17 votes
Accepted

Prove that $\int_{E}f =\lim \int_{E}f_{n}$

17 votes
Accepted

A uniformly bounded local martingale is a martingale

17 votes
Accepted

Infinitesimal Generator of Ito Diffusion Process

17 votes
Accepted

If $0 \in G$ is an open subset of $\mathbb{R}$ and if $ x + y \in G$ for all $x, y\in G $ then $G=\mathbb{R}$.

17 votes

What is meant by a filtration "contains the information" until time $t$?

16 votes
Accepted

The Lévy-Khintchine formula and integrability conditions of a random measure

16 votes

Generated $\sigma$-algebras with cylinder set doesn't contain the space of continuous functions

16 votes
Accepted

Sample variance converge almost surely

15 votes

Expected hitting time of given level by Brownian motion

15 votes
Accepted

Which inequalities are there with stochastic integration?

15 votes

How do I prove that a martingale has a constant expected value?

14 votes

Calculate $\mathbb{E}(W_t^k)$ for a Brownian motion $(W_t)_{t \geq0}$ using Itô's Lemma

14 votes
Accepted

Do moments define distributions?

14 votes

Difference between Modification and Indistinguishable

14 votes
Accepted

Hermite Polynomials and Brownian motion

14 votes
Accepted

What are some easier books for studying martingale?

13 votes
Accepted

Prove that there exists a Borel measurable function $h: \mathbb R \to \mathbb R$ such that $g= h\circ f$.

13 votes
Accepted

Exercises with solutions on Elementary Measure Theory

13 votes
Accepted

Consistency Conditions of the Kolmogorov Extension Theorem

13 votes
Accepted

running maximum of brownian motion and reflected brownian motion

13 votes
Accepted

How to compute $E[W_t^4]$, with $W_t$ being a standard Wiener process

13 votes
Accepted

Karatzas and Shreve Exercise 1.10

13 votes

Collection of standard facts about convergence of random variables

13 votes

Show that $\sin(z)$ is analytic

12 votes
Accepted

Square Integrable local martingale or locally square integrable martingale?

12 votes
Accepted

Additive but not $\sigma$-additive function

12 votes

$X$ and $Y$ i.i.d., $X+Y$ and $X-Y$ independent, $\mathbb{E}(X)=0 $ and $\mathbb{E}(X^2)=1$. Show $X \sim N(0,1)$

12 votes
Accepted

Strong Markov property of Brownian motion

12 votes
Accepted

A planar Brownian motion has area zero

12 votes
Accepted

Martingale oscillating between three values

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