List questions from stochastic-calculus

403

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Proving that $X^2- [X]$ is a local martingale given that $X$ is a cadlag locally square-integrable martingale

Published on 12 Apr 2026 - 0:09

145

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$L^p$ integrable local martingale is still $L^p$ integrable when stopped at localizing stopping times.

Published on 30 Mar 2026 - 3:38

131

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Stock Price Dynamics correlated with Bond market returns

Published on 27 Mar 2026 - 8:58

53

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Does the quadratic covariation process define a measure?

Published on 10 Apr 2026 - 6:46

76

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Distribution of Hitting Times

Published on 06 Feb 2016 - 19:44

399

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Convergence of stochastic processes via convergence of infinitesimal generators

Published on 07 Feb 2016 - 0:39

1k

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How to prove that the following process is a Martingale using Ito's formula?

Published on 09 Apr 2026 - 2:39

274

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Ito Formula for Stochastic Integral

Published on 11 Apr 2026 - 10:58

232

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A computation using the Ito integral

Published on 03 Apr 2026 - 7:08

1.4k

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Which inequalities are there with stochastic integration?

Published on 10 Apr 2026 - 2:31

532

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If $dX_{t} = X_{t}\,dt + \,dB_{t}$, why does $e^{- t}dX_{t} = e^{-t} X_{t} \,dt + e^{-t} \,dB_{t}$?

Published on 09 Feb 2016 - 16:18

2.3k

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How to calculate the PSD of a stochastic process

Published on 11 Apr 2026 - 23:01

87

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For a stopping time $T$, prove that $X^T_t = \mathbb{E}\left[X_T\mid \mathcal{F}_t\right]$

Published on 11 Feb 2016 - 1:04

129

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Compute $\frac{d}{dt}\int_0^t e^{x(s)}ds$, where $x$ is a standard Brownian motion.

Published on 13 Apr 2026 - 1:26

1.3k

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Prove that a process with independent increments and a constant mean is a martingale

Published on 06 Apr 2026 - 5:17

List Question

Proving that $X^2- [X]$ is a local martingale given that $X$ is a cadlag locally square-integrable martingale

$L^p$ integrable local martingale is still $L^p$ integrable when stopped at localizing stopping times.

Stock Price Dynamics correlated with Bond market returns

Does the quadratic covariation process define a measure?

Distribution of Hitting Times

Convergence of stochastic processes via convergence of infinitesimal generators

How to prove that the following process is a Martingale using Ito's formula?

Ito Formula for Stochastic Integral

A computation using the Ito integral

Which inequalities are there with stochastic integration?

If $dX_{t} = X_{t}\,dt + \,dB_{t}$, why does $e^{- t}dX_{t} = e^{-t} X_{t} \,dt + e^{-t} \,dB_{t}$?

How to calculate the PSD of a stochastic process

For a stopping time $T$, prove that $X^T_t = \mathbb{E}\left[X_T\mid \mathcal{F}_t\right]$

Compute $\frac{d}{dt}\int_0^t e^{x(s)}ds$, where $x$ is a standard Brownian motion.

Prove that a process with independent increments and a constant mean is a martingale

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