List questions from stochastic-differential-equations

Published on 05 Sep 2022 - 22:45

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Prove discrete Markov chain $x_i = \sqrt{1-\beta_i} x_{i-1} + \sqrt{\beta_i} z_{i-1}$ converges to $dx=-\frac{1}{2}\beta(t)xdt + \sqrt{\beta(t)} dw$.

Published on 07 Sep 2022 - 12:59

26

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Determine the natural filtration of a given stochastic process

Published on 27 Mar 2026 - 6:10

91

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Almost sure equivalence of regular conditonal probability of a progressive process in a controlled SDE equation.

Published on 08 Sep 2022 - 13:01

27

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definition of stochastic diferential equation

Published on 11 Sep 2022 - 17:09

419

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Why is Itô integration not a "pathwise solution theory" to SDEs, but rough path theory is?

Published on 12 Sep 2022 - 3:24

485

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Density of hitting time for a two-sided barrior for Brownian motion with drift

Published on 18 Sep 2022 - 12:51

53

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Can we show that for any $s > t ≥ 0$, we have $\mathbb{E}[\omega_s|\omega_t] =e^{\kappa(s−t)}\omega_t$ and why?

Published on 21 Sep 2022 - 10:19

189

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How can Wiener process be integrated w.r.t. time?

Published on 22 Sep 2022 - 15:00

188

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Stochastic process with Student's t-distribution

Published on 26 Sep 2022 - 14:31

98

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Why is it possible to substitute in differential form?

Published on 28 Sep 2022 - 8:14

63

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Conditional expectation of the exponential of the integral of a diffusion

Published on 28 Sep 2022 - 8:42

163

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Deriving PDE from stochastic representation formula

Published on 06 Oct 2022 - 21:13

113

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Standard Estimates for SDE

Published on 10 Oct 2022 - 18:21

71

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Calculating expectation of product of two Cox-Ingersoll-Ross (CIR) processes

Published on 12 Oct 2022 - 13:46

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Converting SDE to ODE via Dynkin's formula

Prove discrete Markov chain $x_i = \sqrt{1-\beta_i} x_{i-1} + \sqrt{\beta_i} z_{i-1}$ converges to $dx=-\frac{1}{2}\beta(t)xdt + \sqrt{\beta(t)} dw$.

Determine the natural filtration of a given stochastic process

Almost sure equivalence of regular conditonal probability of a progressive process in a controlled SDE equation.

definition of stochastic diferential equation

Why is Itô integration not a "pathwise solution theory" to SDEs, but rough path theory is?

Density of hitting time for a two-sided barrior for Brownian motion with drift

Can we show that for any $s > t ≥ 0$, we have $\mathbb{E}[\omega_s|\omega_t] =e^{\kappa(s−t)}\omega_t$ and why?

How can Wiener process be integrated w.r.t. time?

Stochastic process with Student's t-distribution

Why is it possible to substitute in differential form?

Conditional expectation of the exponential of the integral of a diffusion

Deriving PDE from stochastic representation formula

Standard Estimates for SDE

Calculating expectation of product of two Cox-Ingersoll-Ross (CIR) processes

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