List questions from brownian-motion

Published on 02 Jun 2020 - 4:10

89

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If $A_t = cos(X_t)$ and $B_t = sin(X_t)$ find the infinitesimal increment for $Y_t = A_t^2 + B_t^2$

Published on 03 Apr 2026 - 1:01

1.9k

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Infinitesimal generator of the standard Brownian motion

Published on 26 Mar 2026 - 18:50

336

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Quadratic variation of $ X_t = t W_t $

Published on 23 Feb 2026 - 6:39

315

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If $t\mapsto X_t$ is continuous almost everywhere and $(X_t)$ has independent increments, then $X_t - X_s$ follows a normal distribution?

Published on 03 Jun 2020 - 9:52

1.1k

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How to solve this simple stochastic differential equation (SDE) $dX_t=-\frac{X_t}{1-t}dt+dB_t$? (hint included)

Published on 26 Mar 2026 - 18:51

99

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$\int_0^t W_s \, ds $ has finite variation

Published on 23 Feb 2026 - 6:42

210

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Does the Martingale Representation theorem hold both ways?

Published on 26 Mar 2026 - 6:18

20

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If $W$ is a Brownian motion, then how can I justify a statement about $\Delta W_{t_{i+1}^{n}}^{2}-\Delta t_{i+1}^{n}$

Published on 03 Apr 2026 - 1:01

247

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Quadratic variation of the absolute value of the Brownian motion

Published on 23 Feb 2026 - 6:40

46

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Brownian Motion/Wiener Process Probability

Published on 06 Jun 2020 - 22:37

241

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Application of Tonelli-Fubini Theorem?

Published on 08 Jun 2020 - 8:27

69

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Convergence of integral of function of Brownian Motion

Published on 08 Jun 2020 - 15:35

86

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Expectation of `fractional' Geometric brownian motions

Published on 26 Mar 2026 - 18:50

160

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For a Wiener process $W_t$, show that $\sum_{i=1}^n h_{i-1}\big(W(t_i \wedge t) - W(t_{i-1}\wedge t)\big), \ t\ge 0$ is a martingale

Published on 01 Apr 2026 - 6:11

List Question

Functions within Expectation of Brownian Motion

If $A_t = cos(X_t)$ and $B_t = sin(X_t)$ find the infinitesimal increment for $Y_t = A_t^2 + B_t^2$

Infinitesimal generator of the standard Brownian motion

Quadratic variation of $ X_t = t W_t $

If $t\mapsto X_t$ is continuous almost everywhere and $(X_t)$ has independent increments, then $X_t - X_s$ follows a normal distribution?

How to solve this simple stochastic differential equation (SDE) $dX_t=-\frac{X_t}{1-t}dt+dB_t$? (hint included)

$\int_0^t W_s \, ds $ has finite variation

Does the Martingale Representation theorem hold both ways?

If $W$ is a Brownian motion, then how can I justify a statement about $\Delta W_{t_{i+1}^{n}}^{2}-\Delta t_{i+1}^{n}$

Quadratic variation of the absolute value of the Brownian motion

Brownian Motion/Wiener Process Probability

Application of Tonelli-Fubini Theorem?

Convergence of integral of function of Brownian Motion

Expectation of `fractional' Geometric brownian motions

For a Wiener process $W_t$, show that $\sum_{i=1}^n h_{i-1}\big(W(t_i \wedge t) - W(t_{i-1}\wedge t)\big), \ t\ge 0$ is a martingale

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