List questions from brownian-motion

Published on 13 Apr 2026 - 21:27

111

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A local martingale subtract half its quadratic variation tends to negative infinity

Published on 13 Apr 2026 - 1:52

93

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Showing that a function of two brownian motions is a martingale.

Published on 14 Apr 2026 - 14:55

327

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Is Brownian motion a semimartingale?

Published on 14 Apr 2026 - 14:52

165

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Question from Exercise 3.3.17 in Karatzas and Shreve. Levy’s characterization theorem

Published on 16 Apr 2026 - 6:28

145

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Surprisingly simple expected time for the "range" of a Brownian motion to extend beyond $a$ - is there a martingale method?

Published on 14 Apr 2026 - 14:56

274

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Hitting time for 2-dimensional Brownian motion

Published on 11 Apr 2026 - 20:54

158

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The stochastic differential of $\cos (B_t^{(1)}B_t^{(2)})$

Published on 16 Apr 2026 - 12:10

160

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Variance of Stock Price - St - given by GBM

Published on 16 Apr 2026 - 6:20

55

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Expect return of a standard Brownian motion

Published on 12 Apr 2026 - 18:46

80

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Supremum of Brownian motion increments

Published on 14 Apr 2026 - 14:55

31

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Expectation of a brownian motion given two states

Published on 14 Apr 2026 - 3:45

33

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Proving $E\bigg[\bigg(\int_a^b X_s dW_s \bigg)^2 \ \bigg\vert \ \mathcal{F}_a \bigg] =\int_a^b (X_s)^2 ds $

Published on 16 Apr 2026 - 23:23

92

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How do I prove that the distribution of $x_t$ in $x_t=x_{t-1}e^{-μt}+ θ(1-e^{-μΔt}) + \int_{t-1}^t e^{-μ(t-s)}\sigma dB_s $ is a normal distribution?

Published on 16 Apr 2026 - 11:31

106

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Distribution of stochastic integral to stopping time

Published on 11 Apr 2026 - 7:09

List Question

The tail $\sigma$-field of Brownian motion

A local martingale subtract half its quadratic variation tends to negative infinity

Showing that a function of two brownian motions is a martingale.

Is Brownian motion a semimartingale?

Question from Exercise 3.3.17 in Karatzas and Shreve. Levy’s characterization theorem

Surprisingly simple expected time for the "range" of a Brownian motion to extend beyond $a$ - is there a martingale method?

Hitting time for 2-dimensional Brownian motion

The stochastic differential of $\cos (B_t^{(1)}B_t^{(2)})$

Variance of Stock Price - St - given by GBM

Expect return of a standard Brownian motion

Supremum of Brownian motion increments

Expectation of a brownian motion given two states

Proving $E\bigg[\bigg(\int_a^b X_s dW_s \bigg)^2 \ \bigg\vert \ \mathcal{F}_a \bigg] =\int_a^b (X_s)^2 ds $

How do I prove that the distribution of $x_t$ in $x_t=x_{t-1}e^{-μt}+ θ(1-e^{-μΔt}) + \int_{t-1}^t e^{-μ(t-s)}\sigma dB_s $ is a normal distribution?

Distribution of stochastic integral to stopping time

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