List questions from stochastic-calculus

Published on 25 Mar 2026 - 14:33

261

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Why in SDE, we always consider the density $p(x,t|x_0)$ and never $p(x,t)$?

Published on 06 Jun 2019 - 19:16

276

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Intuitive reason on how predictable processes are defined

Published on 07 Jun 2019 - 14:22

28

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Limit of expectation of stochastic process

Published on 08 Jun 2019 - 3:08

83

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Prove that the first derivative of expectation is increasing

Published on 08 Jun 2019 - 16:11

71

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Mixed Poisson process $\sim\operatorname{Poisson}(p(t)\lambda)$

Published on 26 Mar 2026 - 11:16

260

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Show a stochastic process is a Martingale

Published on 28 Mar 2026 - 1:25

256

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Showing Ito's formula gives a semimartingale decomposition for brownian motion

Published on 26 Mar 2026 - 14:20

3.4k

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First variation on Brownian motion

Published on 28 Mar 2026 - 1:26

78

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$E[(\int_{0}^{\infty}f(t)dW_t)^2]$ for $f(t)=(W_2-W_1)1_{[2,3)}(t)+(W_3-W_1)1_{[3,5)}(t)$

Published on 28 Mar 2026 - 3:03

26

Views

Derivation of the expectation of an exponential

Published on 26 Mar 2026 - 12:36

431

Views

Characterization of Brownian Motion (Problem Karatzas/Shreve)

Published on 28 Mar 2026 - 4:34

16

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Reconstructing From Conditionals

Published on 14 Jun 2019 - 19:26

134

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Expectation of the exponent of a constant times exiting time of a Brownian motion (i.e. $\mathbb{E}_x[e^{n\sigma}]$)

Published on 25 Mar 2026 - 22:05

878

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Brownian motion and Running Maximum

Published on 28 Mar 2026 - 3:00

List Question

A question on the application of Ito's lemma

Why in SDE, we always consider the density $p(x,t|x_0)$ and never $p(x,t)$?

Intuitive reason on how predictable processes are defined

Limit of expectation of stochastic process

Prove that the first derivative of expectation is increasing

Mixed Poisson process $\sim\operatorname{Poisson}(p(t)\lambda)$

Show a stochastic process is a Martingale

Showing Ito's formula gives a semimartingale decomposition for brownian motion

First variation on Brownian motion

$E[(\int_{0}^{\infty}f(t)dW_t)^2]$ for $f(t)=(W_2-W_1)1_{[2,3)}(t)+(W_3-W_1)1_{[3,5)}(t)$

Derivation of the expectation of an exponential

Characterization of Brownian Motion (Problem Karatzas/Shreve)

Reconstructing From Conditionals

Expectation of the exponent of a constant times exiting time of a Brownian motion (i.e. $\mathbb{E}_x[e^{n\sigma}]$)

Brownian motion and Running Maximum

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