List questions from stochastic-integrals

Published on 09 Apr 2026 - 2:48

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Prove $\mathbb{E}[e^{i \lambda W_t}-1] = -\frac{\lambda^2}{2} \mathbb{E}\left[ \int_0^te^{i\lambda W_s}ds\right]$, where $W_t$ is Brownian motion?

Published on 15 Apr 2026 - 12:26

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Representation of Ito integral

Published on 08 Apr 2026 - 18:07

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Covariance between Wiener process and stochastic integral

Published on 12 Apr 2026 - 10:12

386

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$X_t$ is a cadlag semimartingale implies $f(X_t)$ is a semimartingale by using Ito's Lemma

Published on 12 Apr 2026 - 5:39

113

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Why do we need absolute continuity of the mapping $t \mapsto \langle M \rangle_t(\omega)$ wr.t to the Lebesgue measure for almost all $\omega$?

Published on 15 Apr 2026 - 17:28

96

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Prove that $X_t$ of the given SDE converges to $0$ a.s. as $t\uparrow 1$

Published on 10 May 2026 - 15:03

580

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When is the quadratic variation of a process continuously differentiable?

Published on 12 Apr 2026 - 18:04

203

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Functional CLT proof Theorem 7.4.1 on page 354-355 of Ethier and Kurtz 1986

Published on 15 Apr 2026 - 9:30

437

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Seriously struggling with Ito's lemma, and understanding what this paper does!!!

Published on 29 Apr 2026 - 12:51

95

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Kolmogorovs Extension Theorem

Published on 14 Apr 2026 - 11:13

160

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Proof of martingale representation theorem

Published on 10 Apr 2026 - 23:54

226

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Intuition behind quadratic variation in Brownian motion and $L^2(P)$ convergence for Ito integral

Published on 13 Apr 2026 - 18:14

1.7k

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Find the transition probability function P(y,t,x,s) for Brownian motion with drift B(t)+t.

Published on 13 Apr 2026 - 0:31

167

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What converses exists for Martingale representation theorem?

Published on 12 Apr 2026 - 8:35

List Question

is integral with respect to finite variation process of finite variation?

Prove $\mathbb{E}[e^{i \lambda W_t}-1] = -\frac{\lambda^2}{2} \mathbb{E}\left[ \int_0^te^{i\lambda W_s}ds\right]$, where $W_t$ is Brownian motion?

Representation of Ito integral

Covariance between Wiener process and stochastic integral

$X_t$ is a cadlag semimartingale implies $f(X_t)$ is a semimartingale by using Ito's Lemma

Why do we need absolute continuity of the mapping $t \mapsto \langle M \rangle_t(\omega)$ wr.t to the Lebesgue measure for almost all $\omega$?

Prove that $X_t$ of the given SDE converges to $0$ a.s. as $t\uparrow 1$

When is the quadratic variation of a process continuously differentiable?

Functional CLT proof Theorem 7.4.1 on page 354-355 of Ethier and Kurtz 1986

Seriously struggling with Ito's lemma, and understanding what this paper does!!!

Kolmogorovs Extension Theorem

Proof of martingale representation theorem

Intuition behind quadratic variation in Brownian motion and $L^2(P)$ convergence for Ito integral

Find the transition probability function P(y,t,x,s) for Brownian motion with drift B(t)+t.

What converses exists for Martingale representation theorem?

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