List questions from stochastic-integrals

Published on 30 Apr 2021 - 16:18

359

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Problems solving the SDE $dX_t = aX_tdt +\sigma dB_t$. Why don't Ito's lemma work?

Published on 31 Mar 2026 - 7:30

120

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Solving this integral with minimum function

Published on 02 May 2021 - 9:57

119

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Showing that $X_t=\int_0^t e^{A(t-s)}KX_s\,dB_s+\int_0^te^{A(t-s)}M\,dB_s$ satisfies $dX_t$

Published on 03 May 2021 - 23:25

59

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Proof in Oksendal Book

Published on 03 Apr 2026 - 3:34

46

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Predictable Representation Property of a random variable involving Brownian motion

Published on 07 May 2021 - 10:50

219

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False proof: Every continuous-time financial market has arbitrage.

Published on 31 Mar 2026 - 22:49

604

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Explicit distribution of the d-dimensional Ornstein-Uhlenbeck process

Published on 23 Feb 2026 - 11:46

35

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Help me understand the following equality $\mathbb{E} [e^{\lambda a_i g_i}] = e^{\lambda^2 a_i^2/2}$

Published on 11 May 2021 - 12:32

458

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Proving that the solution to the Cox-Ingersoll-Ross SDE is positive.

Published on 31 Mar 2026 - 9:56

93

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Doob-Meyer decomposition; uniqueness

Published on 31 Mar 2026 - 7:26

126

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Uniqueness of the representation of Ito processes for $G \in \mathcal{L}_2^\text{loc}$

Published on 13 May 2021 - 9:08

156

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Can a stochastic integral be martingale with respect to two different filtrations?

Published on 13 May 2021 - 13:36

89

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Expected value of a product of function and stochastic integral that depend on a solution of SDE

Published on 31 Mar 2026 - 9:55

20

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How to find the variance of stochastic integration

Published on 03 Apr 2026 - 19:29

List Question

Properties of the stochastic integral $\int_0^t\frac{|B_s|}{s}\Bbb dB_s$

Problems solving the SDE $dX_t = aX_tdt +\sigma dB_t$. Why don't Ito's lemma work?

Solving this integral with minimum function

Showing that $X_t=\int_0^t e^{A(t-s)}KX_s\,dB_s+\int_0^te^{A(t-s)}M\,dB_s$ satisfies $dX_t$

Proof in Oksendal Book

Predictable Representation Property of a random variable involving Brownian motion

False proof: Every continuous-time financial market has arbitrage.

Explicit distribution of the d-dimensional Ornstein-Uhlenbeck process

Help me understand the following equality $\mathbb{E} [e^{\lambda a_i g_i}] = e^{\lambda^2 a_i^2/2}$

Proving that the solution to the Cox-Ingersoll-Ross SDE is positive.

Doob-Meyer decomposition; uniqueness

Uniqueness of the representation of Ito processes for $G \in \mathcal{L}_2^\text{loc}$

Can a stochastic integral be martingale with respect to two different filtrations?

Expected value of a product of function and stochastic integral that depend on a solution of SDE

How to find the variance of stochastic integration

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