List questions from stochastic-analysis

Published on 30 Mar 2026 - 14:57

117

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How to define colored noise or noise with correlation?

Published on 25 Dec 2023 - 21:51

50

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Is this map measurable?

Published on 28 Dec 2023 - 8:51

77

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Expected Value of Ito process

Published on 28 Mar 2026 - 15:45

25

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sum of function of stopping times

Published on 30 Dec 2023 - 4:31

49

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Changing order of expectation and integration

Published on 30 Dec 2023 - 5:16

43

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Stratonovich SDE and main hint for Ito's lemma

Published on 28 Mar 2026 - 15:46

71

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Prove directly from the definition of the Wiener process: $\mathbb P \left( \{W_{n^2}\}_{n=1}^{\infty} \text{ is a bounded sequence } \right) = 0$

Published on 03 Jan 2024 - 10:38

109

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Show that $Y_t=\int_0^t \left( \int_0^s (s-u) dW_u \right) dW_s$ is well defined and calculate $\mathbb EY_t$, $\mathbb EY_t^2$

Published on 30 Mar 2026 - 15:00

50

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Space of $f$ for infinitesimal generator of Brownian motion

Published on 05 Jan 2024 - 12:36

52

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A question regarding the analytic expression of an Ito integral

Published on 30 Mar 2026 - 16:45

50

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Show that for $0<b<1<a$: $\mathbb P(\tau_a < \tau_b)=\frac{1-b^4}{a^4-b^4}$

Published on 29 Mar 2026 - 8:15

84

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The Stratonovich operator application

Published on 09 Jan 2024 - 15:42

46

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Bound on the conditional expectation of a stochastic integral given W_T (multidimensional case)

Published on 10 Jan 2024 - 9:45

144

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Calculate $\mathbb EX$, $VarX$ for $\tau=\inf \{t>0: \int_0^t e^{-(W_2^2+2W_s)}ds=2\}, X=\int_0^{\tau}e^{-(\frac{W_s^2}2+W_s)}dW_s$

Published on 29 Mar 2026 - 8:16

List Question

The importance of Itô-integral construction

How to define colored noise or noise with correlation?

Is this map measurable?

Expected Value of Ito process

sum of function of stopping times

Changing order of expectation and integration

Stratonovich SDE and main hint for Ito's lemma

Prove directly from the definition of the Wiener process: $\mathbb P \left( \{W_{n^2}\}_{n=1}^{\infty} \text{ is a bounded sequence } \right) = 0$

Show that $Y_t=\int_0^t \left( \int_0^s (s-u) dW_u \right) dW_s$ is well defined and calculate $\mathbb EY_t$, $\mathbb EY_t^2$

Space of $f$ for infinitesimal generator of Brownian motion

A question regarding the analytic expression of an Ito integral

Show that for $0<b<1<a$: $\mathbb P(\tau_a < \tau_b)=\frac{1-b^4}{a^4-b^4}$

The Stratonovich operator application

Bound on the conditional expectation of a stochastic integral given W_T (multidimensional case)

Calculate $\mathbb EX$, $VarX$ for $\tau=\inf \{t>0: \int_0^t e^{-(W_2^2+2W_s)}ds=2\}, X=\int_0^{\tau}e^{-(\frac{W_s^2}2+W_s)}dW_s$

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