List questions from stochastic-calculus

Published on 11 Dec 2023 - 22:11

100

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How to simulate from $dY_i=Y_i( \mu dt$ $+ \sigma_{(2)}( \alpha dB^{(1)}_i + \sqrt{1- \alpha ^2} dB^{(2)}_i))$ for $\mu, \sigma>0, \alpha \in [-1,1]$?

Published on 26 Mar 2026 - 8:02

107

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Why does the Yamada-Watanabe Uniqueness Theorem for SDEs not hold in the multidimensional case?

Published on 28 Mar 2026 - 14:05

76

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Understanding a proof of the covariance matrix of a random process in SDE

Published on 29 Mar 2026 - 3:35

79

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Expectation Value of n Bernoulli Variables

Published on 28 Mar 2026 - 1:46

54

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Stochastic integral of continuous integrand with bounded variation

Published on 30 Mar 2026 - 13:20

47

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Relationship between $p$ and $q$ variation.

Published on 27 Mar 2026 - 8:39

56

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What should I study to prepare for Stochastic Calculus

Published on 27 Mar 2026 - 8:44

71

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Karatzas & Shreve, Problem 2.22, Positivity of Stopping Time

Published on 26 Mar 2026 - 12:36

16

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Stochastic Differential Equation calculating E(X-1(t))

Published on 09 Mar 2026 - 14:26

43

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Extrinsic Brownian Motion on Manifold

Published on 07 Apr 2026 - 10:59

66

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Let $( W_t )$ be the standard Brownian Motion then solve $\int_0^T (W_t)^5 dW_t$

Published on 30 Mar 2026 - 13:21

39

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Let $X_t = \int_0^t \sin(1 + 3W_s) dW_s$. (1) Find an expression for $X_t$, using Ito's formula. (2) Find mean and variance for $X_t$

Published on 01 Apr 2026 - 23:34

73

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Monotone convergence for $E(\sum_{k}|X_{n_{k}}|)=\sum_{k}E(|X_{n_{k}}|)$

Published on 20 Dec 2023 - 12:46

43

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Spatial discretization of Brownian motion/Wiener process

Published on 28 Mar 2026 - 13:59

List Question

Solution of a linear stochastic equation with multiplicative noise in front of the derivative

How to simulate from $dY_i=Y_i( \mu dt$ $+ \sigma_{(2)}( \alpha dB^{(1)}_i + \sqrt{1- \alpha ^2} dB^{(2)}_i))$ for $\mu, \sigma>0, \alpha \in [-1,1]$?

Why does the Yamada-Watanabe Uniqueness Theorem for SDEs not hold in the multidimensional case?

Understanding a proof of the covariance matrix of a random process in SDE

Expectation Value of n Bernoulli Variables

Stochastic integral of continuous integrand with bounded variation

Relationship between $p$ and $q$ variation.

What should I study to prepare for Stochastic Calculus

Karatzas & Shreve, Problem 2.22, Positivity of Stopping Time

Stochastic Differential Equation calculating E(X-1(t))

Extrinsic Brownian Motion on Manifold

Let $( W_t )$ be the standard Brownian Motion then solve $\int_0^T (W_t)^5 dW_t$

Let $X_t = \int_0^t \sin(1 + 3W_s) dW_s$. (1) Find an expression for $X_t$, using Ito's formula. (2) Find mean and variance for $X_t$

Monotone convergence for $E(\sum_{k}|X_{n_{k}}|)=\sum_{k}E(|X_{n_{k}}|)$

Spatial discretization of Brownian motion/Wiener process

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