User Calculon

10 votes

1 answer

3k views

Joint distribution of Brownian motion and its running maximum

asked Aug 9, 2015 at 20:26

10 votes

3 answers

2k views

Quadratic variation of the Ornstein-Uhlenbeck process

asked Aug 9, 2015 at 21:07

10 votes

2 answers

284 views

How to evaluate $\int_0^\infty\frac{ \sin{x}}{x^2+1}dx$?

asked Feb 5, 2022 at 17:02

8 votes

2 answers

2k views

Laplace transform of hitting time of Brownian motion with drift

asked Feb 13, 2018 at 19:22

7 votes

1 answer

3k views

Asymptotic joint distribution of sample mean and sample variance

asked Sep 14, 2016 at 19:00

7 votes

1 answer

2k views

Integral of square of Brownian motion with respect to Brownian Motion

asked Mar 21, 2015 at 16:15

6 votes

0 answers

408 views

Application of Doob's optional stopping theorem to an elementary probability problem

asked Feb 9, 2016 at 15:26

6 votes

2 answers

717 views

Linear transform of a strictly stationary time series

asked Apr 24, 2016 at 21:42

5 votes

1 answer

345 views

Convergence of moments of a sequence of random variables

asked Apr 24, 2016 at 20:56

5 votes

1 answer

2k views

Examples of predictable processes

asked May 17, 2015 at 12:51

5 votes

1 answer

220 views

Integrating over a power of the infinitesimal

asked Oct 31, 2014 at 14:48

5 votes

1 answer

225 views

Jointly nilpotent matrices

asked Mar 12, 2015 at 20:53

5 votes

2 answers

2k views

Integral of time with respect to Brownian motion

asked Mar 20, 2015 at 12:23

4 votes

0 answers

2k views

Integral of Brownian Motion with respect to an independent Brownian motion

asked May 25, 2015 at 21:09

4 votes

1 answer

3k views

Brownian motion at infinity

asked May 16, 2015 at 13:33

4 votes

0 answers

56 views

An inequality regarding the expectation of a transformed random variable

asked Jan 29, 2016 at 13:38

4 votes

1 answer

119 views

Finiteness of the sum of the product of an i.i.d. sequence

asked Jun 30, 2015 at 20:41

4 votes

1 answer

649 views

A martingale characterization

asked Sep 18, 2015 at 10:40

4 votes

1 answer

2k views

Approximating a discontinuous by a smooth function

asked Sep 8, 2016 at 16:25

4 votes

1 answer

387 views

Measurability of the zero-crossing time of Brownian motion

asked Mar 11, 2016 at 21:49

4 votes

1 answer

101 views

Fundamental theorem of calculus for semigroups

asked Apr 9, 2018 at 13:59

4 votes

1 answer

841 views

Hitting time of Brownian motion against a square root curve

asked Apr 24, 2018 at 18:24

4 votes

2 answers

235 views

Eigenvalues of a polynomial of a matrix

asked May 23, 2018 at 18:38

4 votes

1 answer

906 views

Linearity of convergence in probability

asked Feb 25, 2015 at 11:01

3 votes

0 answers

247 views

Mutual independence of increments of Brownian motion

asked May 9, 2015 at 11:26

3 votes

0 answers

118 views

A sequence for which the running average converges to something other than the expected value

asked Aug 29, 2018 at 14:40

3 votes

2 answers

155 views

Almost surely infinite random variable

asked Sep 12, 2021 at 10:17

3 votes

1 answer

166 views

Preservation of the Markov property

asked Mar 23, 2018 at 15:11

3 votes

0 answers

483 views

Return of 2D Brownian motion to the origin

asked Mar 30, 2018 at 20:53

3 votes

1 answer

390 views

Proof that a random measure with orthogonal increments is a measure

asked Jul 19, 2015 at 18:03

Stack Exchange Network

129 Questions

Joint distribution of Brownian motion and its running maximum

Quadratic variation of the Ornstein-Uhlenbeck process

How to evaluate $\int_0^\infty\frac{ \sin{x}}{x^2+1}dx$?

Laplace transform of hitting time of Brownian motion with drift

Asymptotic joint distribution of sample mean and sample variance

Integral of square of Brownian motion with respect to Brownian Motion

Application of Doob's optional stopping theorem to an elementary probability problem

Linear transform of a strictly stationary time series

Convergence of moments of a sequence of random variables

Examples of predictable processes

Integrating over a power of the infinitesimal

Jointly nilpotent matrices

Integral of time with respect to Brownian motion

Integral of Brownian Motion with respect to an independent Brownian motion

Brownian motion at infinity

An inequality regarding the expectation of a transformed random variable

Finiteness of the sum of the product of an i.i.d. sequence

A martingale characterization

Approximating a discontinuous by a smooth function

Measurability of the zero-crossing time of Brownian motion

Fundamental theorem of calculus for semigroups

Hitting time of Brownian motion against a square root curve

Eigenvalues of a polynomial of a matrix

Linearity of convergence in probability

Mutual independence of increments of Brownian motion

A sequence for which the running average converges to something other than the expected value

Almost surely infinite random variable

Preservation of the Markov property

Return of 2D Brownian motion to the origin

Proof that a random measure with orthogonal increments is a measure