User Falrach

17 votes

1 answer

429 views

Is this distribution already known and has a name?

asked Dec 5, 2019 at 16:50

10 votes

1 answer

497 views

Is this function decreasing in $x$?

calculus integration inequality integral-inequality error-function

asked Jul 7, 2019 at 13:00

8 votes

1 answer

243 views

Law of brownian hitting time uniquely determined by the barrier?

probability probability-theory brownian-motion

asked Sep 27, 2019 at 11:47

4 votes

2 answers

114 views

Do I have a chance to get a closed form for this integral?

integration definite-integrals asymptotics closed-form

asked Jun 6, 2019 at 14:06

4 votes

4 answers

303 views

Smooth Logarithm at zero/one with special conditions

real-analysis analysis derivatives logarithms

asked Jun 1, 2018 at 13:25

3 votes

1 answer

179 views

Kolmogorov extension theorem for measures on the space of continuous functions

probability-theory measure-theory stochastic-processes

asked Jan 4, 2019 at 15:11

3 votes

1 answer

96 views

Compactness of a specific set in weak topology

general-topology functional-analysis measure-theory weak-convergence topological-vector-spaces

asked Jan 8, 2019 at 18:07

3 votes

1 answer

153 views

Dominated convergence theorem applied to the convergence of measures

measure-theory probability-distributions weak-convergence

asked Jun 21, 2019 at 9:08

2 votes

2 answers

95 views

How to determine whether $\Bbb P ( B_{t_1} \in [x - c , x + c ], \ldots , B_{t_n} \in [x -c , x + c ])$ is decreasing in $x$?

probability integration derivatives normal-distribution

asked Jun 26, 2019 at 13:26

2 votes

1 answer

148 views

The $L^1$ distance of two CDF is the $L^1$ distance of the quantile function coupling

probability probability-theory probability-distributions cumulative-distribution-functions quantile-function

asked Oct 11, 2019 at 13:52

2 votes

1 answer

363 views

Calculation Resolvent/$\alpha$-Potential of Brownian Motion/Wiener Process

integration laplace-transform brownian-motion bessel-functions gaussian-integral

asked Apr 20, 2018 at 12:54

2 votes

0 answers

37 views

Expectation of $ | \{ j \in \Bbb N : \sum_{i=1}^j \alpha_i \leq t \} |$ , $\alpha_i$ iid RV on $[0,\infty)$

probability probability-distributions poisson-process

asked Jun 4, 2018 at 20:06

2 votes

1 answer

161 views

Writing a mathematical work in english

article-writing

asked Dec 22, 2017 at 14:05

2 votes

1 answer

140 views

Is there a $t$ such that this function is positive?

normal-distribution roots gaussian-integral

asked Jan 24, 2020 at 15:51

2 votes

3 answers

142 views

References on semicontinuous functions

reference-request semicontinuous-functions

asked Mar 4, 2020 at 18:09

2 votes

1 answer

91 views

Which topology is transferred by this specific metric on the rectangle $[0,\infty] \times [0 , \infty ]$?

general-topology convergence-divergence metric-spaces semicontinuous-functions

asked Jul 27, 2019 at 8:35

2 votes

1 answer

386 views

Kuratowski convergence and Hausdorff metric

general-topology reference-request metric-spaces compactness hausdorff-distance

asked Aug 9, 2019 at 12:34

2 votes

2 answers

143 views

Representation of stochastic integral w.r.t. semimartingale with finitely many jumps in finite time

probability-theory stochastic-calculus stochastic-integrals local-martingales

asked Nov 13, 2019 at 10:22

2 votes

1 answer

55 views

Asymptotic for $\int_0^1 z e^{-\frac{(d+z)^2}{a}} \text d z$ for $a\to 0$.

integration asymptotics

asked Dec 2, 2019 at 16:28

2 votes

0 answers

69 views

A strong law of large numbers for a certain thinned triangular array with weakly correlated random variables.

probability-theory reference-request correlation law-of-large-numbers

asked Sep 21, 2021 at 17:13

2 votes

1 answer

58 views

Prokhorov or probability metric and (gaussian) convolution as Lipschitz functional

probability-theory reference-request convolution lipschitz-functions gaussian

asked Nov 19, 2021 at 11:46

2 votes

1 answer

71 views

Uniform convergence of continuous functions $f_n$ to $f >0$ a.e., implies convergence of Riemann sum involving $1_{(-\infty , 0)}(f_n(s))$

reference-request riemann-integration

asked Dec 1, 2021 at 19:31

2 votes

1 answer

58 views

From which class of continuous distributions on $(0,\infty )$ is $F(t) = 1 - (1 + \frac t 2 )e^{-t}$?

probability-distributions reference-request

asked Jan 20 at 17:11

2 votes

0 answers

45 views

Which explicit expressions for $\Bbb E [ f(Z\sqrt{t} +x)]=\int_{\Bbb R} f(u \sqrt{t} + x) e^{-u^2 /2} du$ are known, where $Z \sim \mathcal{N}(0,1)$?

reference-request normal-distribution closed-form

asked Feb 25 at 16:05

1 vote

1 answer

49 views

Calculation of a specific integral involving the Levy distribution

reference-request definite-integrals closed-form

asked Mar 8 at 18:33

1 vote

0 answers

16 views

Avoiding measurability due to independence

probability-theory

asked May 17 at 10:17

1 vote

1 answer

33 views

Counterexample or ideas for this reweighted mean going to zero.

probability examples-counterexamples law-of-large-numbers

asked Jun 9, 2020 at 15:33

1 vote

1 answer

74 views

Verifying that a computed density is a probability density

probability probability-distributions binomial-coefficients

asked Dec 11, 2020 at 11:01

1 vote

0 answers

36 views

Explicit example of a function given by an implicit equation

normal-distribution implicit-differentiation error-function implicit-function

asked Jan 22, 2021 at 17:19

1 vote

1 answer

41 views

Closed form of inverse of $(0,1) \ni x\mapsto \int_{-\infty }^{- \sqrt{-\log(x)}} e^{-\frac{z^2}{2}} dz + \sqrt{-x\log(x)}$

inverse closed-form inverse-function

asked Mar 24, 2021 at 9:53

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60 Questions

Is this distribution already known and has a name?

Is this function decreasing in $x$?

Law of brownian hitting time uniquely determined by the barrier?

Do I have a chance to get a closed form for this integral?

Smooth Logarithm at zero/one with special conditions

Kolmogorov extension theorem for measures on the space of continuous functions

Compactness of a specific set in weak topology

Dominated convergence theorem applied to the convergence of measures

How to determine whether $\Bbb P ( B_{t_1} \in [x - c , x + c ], \ldots , B_{t_n} \in [x -c , x + c ])$ is decreasing in $x$?

The $L^1$ distance of two CDF is the $L^1$ distance of the quantile function coupling

Calculation Resolvent/$\alpha$-Potential of Brownian Motion/Wiener Process

Expectation of $ | \{ j \in \Bbb N : \sum_{i=1}^j \alpha_i \leq t \} |$ , $\alpha_i$ iid RV on $[0,\infty)$

Writing a mathematical work in english

Is there a $t$ such that this function is positive?

References on semicontinuous functions

Which topology is transferred by this specific metric on the rectangle $[0,\infty] \times [0 , \infty ]$?

Kuratowski convergence and Hausdorff metric

Representation of stochastic integral w.r.t. semimartingale with finitely many jumps in finite time

Asymptotic for $\int_0^1 z e^{-\frac{(d+z)^2}{a}} \text d z$ for $a\to 0$.

A strong law of large numbers for a certain thinned triangular array with weakly correlated random variables.

Prokhorov or probability metric and (gaussian) convolution as Lipschitz functional

Uniform convergence of continuous functions $f_n$ to $f >0$ a.e., implies convergence of Riemann sum involving $1_{(-\infty , 0)}(f_n(s))$

From which class of continuous distributions on $(0,\infty )$ is $F(t) = 1 - (1 + \frac t 2 )e^{-t}$?

Which explicit expressions for $\Bbb E [ f(Z\sqrt{t} +x)]=\int_{\Bbb R} f(u \sqrt{t} + x) e^{-u^2 /2} du$ are known, where $Z \sim \mathcal{N}(0,1)$?

Calculation of a specific integral involving the Levy distribution

Avoiding measurability due to independence

Counterexample or ideas for this reweighted mean going to zero.

Verifying that a computed density is a probability density

Explicit example of a function given by an implicit equation

Closed form of inverse of $(0,1) \ni x\mapsto \int_{-\infty }^{- \sqrt{-\log(x)}} e^{-\frac{z^2}{2}} dz + \sqrt{-x\log(x)}$