Question

Modifying the covariance of Brownian motion, what Gaussian process do we get?

score 406 · Answer 1 · 2026-04-14 11:16:49

406

Views

Modifying the covariance of Brownian motion, what Gaussian process do we get?

Published on 14 Apr 2026 - 11:16

score 122 · Answer 2 · 2026-04-12 03:44:51

122

Views

Connection between elliptic operators, the Martingale problem and diffusion

Published on 12 Apr 2026 - 3:44

score 279 · Answer 3 · 2026-04-11 05:22:01

279

Views

SDE with constant coefficients

Published on 11 Apr 2026 - 5:22

score 42 · Answer 4 · 2026-04-11 23:44:59

42

Views

The mean of the integral of an adapted process

Published on 11 Apr 2026 - 23:44

score 385 · Answer 5 · 2026-04-12 03:51:49

385

Views

For a cadlag submartingale $X$ the function $t \mapsto E[X_{t}]$ is right continuous.

Published on 12 Apr 2026 - 3:51

score 250 · Answer 6 · 2026-04-15 01:07:55

250

Views

Show Geometric Brownian motion is the unique solution to $\frac{dS_t}{S_t}=\mu dt+\sigma dW_t$.

Published on 15 Apr 2026 - 1:07

score 84 · Answer 7 · 2026-04-15 23:26:49

84

Views

Prove that $(\cos(B_t),\sin(B_t))$ is a Brownian motion on the circle.

Published on 15 Apr 2026 - 23:26

score 538 · Answer 8 · 2026-04-14 08:16:15

538

Views

What is the set of stochastic processes that have a deterministic quadratic variation?

Published on 14 Apr 2026 - 8:16

score 558 · Answer 9 · 2026-04-14 10:14:23

558

Views

Kolmogorov Backward and Forward Equations: Why are there different derivations for the forward and backward dynamics?

Published on 14 Apr 2026 - 10:14

score 94 · Answer 10 · 2026-04-29 15:27:57

94

Views

Can we show that a local martingale is closed when it is stopped at one of the localising stopping times?

Published on 29 Apr 2026 - 15:27

score 572 · Answer 11 · 2026-04-12 13:34:52

572

Views

Formula for quadratic variation of a general Levy process

Published on 12 Apr 2026 - 13:34

score 286 · Answer 12 · 2026-04-16 22:47:44

286

Views

Example of $\mathbb{E}[X_t|\mathcal{F}_0]=X_0$ but $X_t$ is not a martingale?

Published on 16 Apr 2026 - 22:47

score 227 · Answer 13 · 2026-04-08 18:28:10

227

Views

Writing a given process as a diffusion

Published on 08 Apr 2026 - 18:28

score 138 · Answer 14 · 2026-04-14 07:04:17

138

Views

How does Ito's formula work at a point where the function/derivative is undefined? E.g. $x=(0,...,0)$ and $f(x)=\lvert x\rvert^{p}$

Published on 14 Apr 2026 - 7:04

score 160 · Answer 15 · 2026-04-29 15:27:49

160

Views

Why is $\sigma(B_{s}-s: 0\leq s\leq t)$ strictly included in $\mathcal{F}_{t}^{B}$

Published on 29 Apr 2026 - 15:27

List Question

Modifying the covariance of Brownian motion, what Gaussian process do we get?

Connection between elliptic operators, the Martingale problem and diffusion

SDE with constant coefficients

The mean of the integral of an adapted process

For a cadlag submartingale $X$ the function $t \mapsto E[X_{t}]$ is right continuous.

Show Geometric Brownian motion is the unique solution to $\frac{dS_t}{S_t}=\mu dt+\sigma dW_t$.

Prove that $(\cos(B_t),\sin(B_t))$ is a Brownian motion on the circle.

What is the set of stochastic processes that have a deterministic quadratic variation?

Kolmogorov Backward and Forward Equations: Why are there different derivations for the forward and backward dynamics?

Can we show that a local martingale is closed when it is stopped at one of the localising stopping times?

Formula for quadratic variation of a general Levy process

Example of $\mathbb{E}[X_t|\mathcal{F}_0]=X_0$ but $X_t$ is not a martingale?

Writing a given process as a diffusion

How does Ito's formula work at a point where the function/derivative is undefined? E.g. $x=(0,...,0)$ and $f(x)=\lvert x\rvert^{p}$

Why is $\sigma(B_{s}-s: 0\leq s\leq t)$ strictly included in $\mathcal{F}_{t}^{B}$

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