List questions from stochastic-integrals

Published on 30 Apr 2022 - 1:04

156

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An application of the multidimensional version of Itô's formula

Published on 02 May 2022 - 10:23

88

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Show that $\mathbb{E}(X|\mathcal{F}_t)$ is a square-integrable martingale

Published on 01 Apr 2026 - 11:21

30

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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 04 May 2022 - 7:55

72

Views

Using BDG inequality to show the solution to a BSDE belongs to $S^2_{\mathscr{F}}$

Published on 01 Apr 2026 - 11:22

99

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Integrating factor and homogeneous equation for SDEs.

Published on 01 Apr 2026 - 11:15

48

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For stochastic integral $I$ of simple process $X$, $0 \le s < t< \infty$, show $E[I_t(X) | \mathscr{F}_s] = I_s(X)$ a.s.

Published on 07 May 2022 - 14:21

104

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Distribution of stochastic integral to stopping time

Published on 03 Apr 2026 - 17:10

81

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Using the BDG inequality to show a process is uniformly integrable

Published on 01 Apr 2026 - 11:16

215

Views

Finding a weak solution to an SDE

Published on 01 Apr 2026 - 11:14

140

Views

Expectation of product of brownian motion and stochastic integral

Published on 08 May 2022 - 18:01

107

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Finding a change of measure so that rescaled local martingale is a local martingale

Published on 01 Apr 2026 - 11:19

350

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Using SDE uniqueness in law to show that two processes have the same distribution

Published on 01 Apr 2026 - 11:21

52

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Expected value of maximum of two numbers, where one is normal distributed

Published on 12 May 2022 - 11:35

322

Views

Constructing the solution to a linear backward SDE

Published on 12 May 2022 - 12:06

List Question

Explicit form of expectation of a function of sum of geometric Brownian motion

An application of the multidimensional version of Itô's formula

Show that $\mathbb{E}(X|\mathcal{F}_t)$ is a square-integrable martingale

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 $

Using BDG inequality to show the solution to a BSDE belongs to $S^2_{\mathscr{F}}$

Integrating factor and homogeneous equation for SDEs.

For stochastic integral $I$ of simple process $X$, $0 \le s < t< \infty$, show $E[I_t(X) | \mathscr{F}_s] = I_s(X)$ a.s.

Distribution of stochastic integral to stopping time

Using the BDG inequality to show a process is uniformly integrable

Finding a weak solution to an SDE

Expectation of product of brownian motion and stochastic integral

Finding a change of measure so that rescaled local martingale is a local martingale

Using SDE uniqueness in law to show that two processes have the same distribution

Expected value of maximum of two numbers, where one is normal distributed

Constructing the solution to a linear backward SDE

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