User saz

43 votes

2 answers

4k views

Collection: Results on stopping times for Brownian motion (with drift)

asked Jan 19, 2019 at 11:06

32 votes

1 answer

2k views

Martingale theory: Collection of examples and counterexamples

asked Oct 28, 2018 at 8:18

18 votes

3 answers

3k views

Existence of iid random variables

asked Dec 3, 2012 at 18:13

11 votes

1 answer

1k views

Weak generator of Feller semigroup

asked Jan 16, 2013 at 18:08

11 votes

2 answers

2k views

Borel $\sigma$-algebras on the Skorohod space $D[0,1]$

asked Feb 13, 2014 at 7:54

11 votes

1 answer

3k views

Approximation of indicator function of an open set by continuous functions

asked Feb 25, 2014 at 19:39

11 votes

0 answers

749 views

Conditions for the existence of a density with respect to Lebesgue measure

asked Sep 12, 2016 at 15:37

10 votes

0 answers

475 views

Holomorphic extensions of characteristic functions

asked Oct 13, 2015 at 15:51

9 votes

1 answer

272 views

Does $\mu(x+B)= \mu(B)$ for all balls $B$ imply that $\mu$ equals the Lebesgue measure (up to scaling)?

asked May 29, 2015 at 16:05

7 votes

1 answer

126 views

Separation of closed sets with distance $>0$ by function $f \in C_b^k(\mathbb{R}^d)$

asked Nov 4, 2018 at 19:10

7 votes

2 answers

2k views

If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$

asked Mar 1, 2013 at 9:11

7 votes

2 answers

2k views

Approximation of stochastic integral

asked Apr 11, 2013 at 9:11

7 votes

2 answers

723 views

Computation of $\int_0^{\pi} \frac{\sin^n \theta}{(1+x^2-2x \cdot \cos \theta)^{\frac{n}{2}}} \, d\theta$

asked May 18, 2013 at 9:35

6 votes

0 answers

547 views

Characterization of the law of a stochastic process by its finite dimensional distributions

asked Jun 15, 2013 at 13:01

6 votes

0 answers

84 views

Generalized Itô's formula for random mappings

asked Sep 30, 2017 at 15:34

5 votes

2 answers

762 views

Which functions can be approximated by Hölder continuous functions in a "bounded way"?

asked Jan 9, 2018 at 16:40

5 votes

0 answers

783 views

Independence of Brownian motion-related stopping times

asked Feb 24, 2013 at 17:54

5 votes

2 answers

350 views

Generalization Of The Binomial Theorem

asked Dec 27, 2012 at 13:05

4 votes

1 answer

231 views

Distribution of a Brownian motion with respect to $\mathbb{P}^x$

asked Apr 27, 2013 at 15:53

4 votes

1 answer

791 views

Application of central limit theorem for triangular arrays

asked Mar 20, 2013 at 14:33

4 votes

2 answers

1k views

Composition of pseudo-differential operators

asked Apr 3, 2013 at 18:26

3 votes

1 answer

638 views

Translational invariance of Brownian motion

asked Jan 9, 2013 at 17:16

3 votes

1 answer

662 views

Clarke Ocone representation formula

asked Dec 10, 2012 at 21:50

3 votes

0 answers

509 views

Lévy measure of a pure jump process

asked Mar 7, 2013 at 20:10

3 votes

1 answer

97 views

Proving $\int_{(1,\infty)} f(s) \, ds < \infty$ by proving the divergence of a certain integral

asked Nov 6, 2017 at 15:53

3 votes

1 answer

407 views

Prove the bound $|f'(x)| \leq c |f(x)|$ for a submultiplicative function$f$

asked Mar 4, 2015 at 15:09

2 votes

1 answer

236 views

Rademacher theorem for 2nd order derivative

asked May 27, 2018 at 15:57

2 votes

1 answer

195 views

Besov spaces: Regularization by convolution

asked Nov 19, 2020 at 20:27

2 votes

1 answer

771 views

Quadratic variation of a purely discontinuous martingale

asked Aug 28, 2013 at 18:43

2 votes

2 answers

169 views

Small time behavior of Lévy processes

asked Oct 28, 2013 at 17:38

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31 Questions

Collection: Results on stopping times for Brownian motion (with drift)

Martingale theory: Collection of examples and counterexamples

Existence of iid random variables

Weak generator of Feller semigroup

Borel $\sigma$-algebras on the Skorohod space $D[0,1]$

Approximation of indicator function of an open set by continuous functions

Conditions for the existence of a density with respect to Lebesgue measure

Holomorphic extensions of characteristic functions

Does $\mu(x+B)= \mu(B)$ for all balls $B$ imply that $\mu$ equals the Lebesgue measure (up to scaling)?

Separation of closed sets with distance $>0$ by function $f \in C_b^k(\mathbb{R}^d)$

If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$

Approximation of stochastic integral

Computation of $\int_0^{\pi} \frac{\sin^n \theta}{(1+x^2-2x \cdot \cos \theta)^{\frac{n}{2}}} \, d\theta$

Characterization of the law of a stochastic process by its finite dimensional distributions

Generalized Itô's formula for random mappings

Which functions can be approximated by Hölder continuous functions in a "bounded way"?

Independence of Brownian motion-related stopping times

Generalization Of The Binomial Theorem

Distribution of a Brownian motion with respect to $\mathbb{P}^x$

Application of central limit theorem for triangular arrays

Composition of pseudo-differential operators

Translational invariance of Brownian motion

Clarke Ocone representation formula

Lévy measure of a pure jump process

Proving $\int_{(1,\infty)} f(s) \, ds < \infty$ by proving the divergence of a certain integral

Prove the bound $|f'(x)| \leq c |f(x)|$ for a submultiplicative function$f$

Rademacher theorem for 2nd order derivative

Besov spaces: Regularization by convolution

Quadratic variation of a purely discontinuous martingale

Small time behavior of Lévy processes