User Chaos

6 votes

0 answers

328 views

How to show this is not a martingale.

asked Jan 30, 2020 at 12:08

6 votes

1 answer

3k views

Calculation of the quadratic variation of an Itô process.

asked Jan 24, 2020 at 11:50

5 votes

0 answers

77 views

"Second order quantization operator" and its role in the construction of Hida spaces.

asked Aug 21, 2020 at 7:19

4 votes

1 answer

116 views

Brownian local time: can we estimate $\mathbb{E}^B\left[\int_{\mathbb{R}}\left|L_{a}(t)-L_{a}(s)\right|^2da\right]$?

asked Oct 15, 2021 at 15:02

4 votes

0 answers

117 views

How to show Tanaka's formula is the Doob-Meyer decomposition?

asked Feb 11, 2020 at 17:39

4 votes

1 answer

191 views

Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

asked Jan 14, 2019 at 14:37

3 votes

0 answers

46 views

for which $\sigma$-algebra this set function is a measure?

asked Aug 21, 2019 at 15:10

3 votes

1 answer

212 views

Polynomial representation: Marsden's Identity.

asked Dec 7, 2018 at 16:04

3 votes

1 answer

150 views

Commutativity relationship between the Malliavin derivative and the Skorkohod divergence operators.

asked May 6, 2020 at 17:26

3 votes

2 answers

373 views

Stereographic projection of "unit sphere" in a Banach space

asked Feb 7, 2021 at 11:09

3 votes

0 answers

192 views

Sufficient condition for weak existence of SDE's solutions.

asked Apr 17, 2020 at 15:16

3 votes

0 answers

49 views

Is this enough to prove that every continuous function $u:\mathbb{R}\rightarrow \mathbb{R}$ is measurable?

asked Sep 4, 2019 at 14:31

3 votes

1 answer

333 views

Doubt regarding definition of integral for positive measurable functions.

asked Sep 7, 2019 at 9:44

2 votes

1 answer

715 views

Multiple Convolution closed form.

asked Nov 22, 2018 at 9:35

2 votes

1 answer

44 views

Any (convergent) sequence of functions in $\mathcal L^p$ that are bounded by a function $w\in\mathcal L^p$ converge in $\mathcal L^p$?

asked Sep 14, 2019 at 10:22

2 votes

1 answer

36 views

Let $u(x)=(x^{\alpha}+x^{\beta})^{-1}$ $x,\alpha,\beta>0$. Find $p\geq 1$, $u\in\mathcal L^p(\lambda^1,(0,\infty))$

asked Oct 29, 2019 at 16:26

2 votes

0 answers

38 views

Obtain unknown matrix from eigendecomposition.

asked Oct 25, 2018 at 13:23

2 votes

2 answers

1k views

Convergence of the inner product in Hilbert Space

asked Nov 6, 2018 at 14:25

2 votes

3 answers

490 views

Orthonormal basis: Countable $\infty$ vs. Uncountable $\infty$

asked Nov 7, 2018 at 18:41

2 votes

2 answers

115 views

Proving that a given function $f^*$ is the best least square approximation

asked Jan 23, 2019 at 10:23

2 votes

1 answer

416 views

Help understanding $D_{KL} (g;f)=0\iff f=g$ a.e.

asked Apr 27, 2020 at 10:08

2 votes

0 answers

191 views

Isonormal Gaussian process associated with a Hilbert space.

asked May 23, 2020 at 9:11

2 votes

1 answer

198 views

On Cameron-Martin space definition.

asked Jul 2, 2020 at 9:15

2 votes

1 answer

260 views

Time derivative of heat semigroup.

asked Sep 22, 2020 at 16:35

2 votes

2 answers

685 views

Expressing Hermite polynomials using confluent hypergeometric functions

asked Apr 3, 2020 at 8:48

2 votes

1 answer

172 views

Compensator for $\bigg(\int_0^t f(s)dB(s)\bigg)^2$.

asked Feb 7, 2020 at 11:54

2 votes

2 answers

51 views

$ \lim_{j\rightarrow \infty}\mu(A_j) \implies \lim_{j\rightarrow \infty}\int_{A_j} u d\mu=0, \forall u\in \mathcal L^1(\mu)$

asked Oct 1, 2019 at 9:52

2 votes

1 answer

766 views

Convolution of distribution functions.

asked Nov 29, 2019 at 16:33

2 votes

1 answer

348 views

Differentiation under integral sign holomorphic function.

asked Apr 10, 2020 at 16:30

2 votes

1 answer

224 views

Continuous square integrable martingale with non-random quadratic variation.

asked Mar 31, 2020 at 9:39

Stack Exchange Network

112 Questions

How to show this is not a martingale.

Calculation of the quadratic variation of an Itô process.

"Second order quantization operator" and its role in the construction of Hida spaces.

Brownian local time: can we estimate $\mathbb{E}^B\left[\int_{\mathbb{R}}\left|L_{a}(t)-L_{a}(s)\right|^2da\right]$?

How to show Tanaka's formula is the Doob-Meyer decomposition?

Estimating Spline curve by OLS. Is a good idea to fix the knots at Chebyshev sites?

for which $\sigma$-algebra this set function is a measure?

Polynomial representation: Marsden's Identity.

Commutativity relationship between the Malliavin derivative and the Skorkohod divergence operators.

Stereographic projection of "unit sphere" in a Banach space

Sufficient condition for weak existence of SDE's solutions.

Is this enough to prove that every continuous function $u:\mathbb{R}\rightarrow \mathbb{R}$ is measurable?

Doubt regarding definition of integral for positive measurable functions.

Multiple Convolution closed form.

Any (convergent) sequence of functions in $\mathcal L^p$ that are bounded by a function $w\in\mathcal L^p$ converge in $\mathcal L^p$?

Let $u(x)=(x^{\alpha}+x^{\beta})^{-1}$ $x,\alpha,\beta>0$. Find $p\geq 1$, $u\in\mathcal L^p(\lambda^1,(0,\infty))$

Obtain unknown matrix from eigendecomposition.

Convergence of the inner product in Hilbert Space

Orthonormal basis: Countable $\infty$ vs. Uncountable $\infty$

Proving that a given function $f^*$ is the best least square approximation

Help understanding $D_{KL} (g;f)=0\iff f=g$ a.e.

Isonormal Gaussian process associated with a Hilbert space.

On Cameron-Martin space definition.

Time derivative of heat semigroup.

Expressing Hermite polynomials using confluent hypergeometric functions

Compensator for $\bigg(\int_0^t f(s)dB(s)\bigg)^2$.

$ \lim_{j\rightarrow \infty}\mu(A_j) \implies \lim_{j\rightarrow \infty}\int_{A_j} u d\mu=0, \forall u\in \mathcal L^1(\mu)$

Convolution of distribution functions.

Differentiation under integral sign holomorphic function.

Continuous square integrable martingale with non-random quadratic variation.