List questions from stochastic-calculus

Published on 28 Mar 2026 - 5:22

209

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Expectation of Brownian hitting time

Published on 28 Mar 2026 - 14:07

695

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Expectation involving local time of Brownian motion

Published on 28 Mar 2026 - 14:05

80

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Local times in higher dimensions

Published on 28 Mar 2026 - 13:59

67

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Prove $E\left[\exp^{ia\int_0^Tf(t) \, dB_t}\right]=\exp\left(-\frac{a^2}{2}\int_0^Tf^2(t) \, dt\right)$

Published on 12 Feb 2020 - 15:53

102

Views

Existence of optional quadratic variation (or quadratic co-variation) [X,Y]

Published on 28 Mar 2026 - 5:22

64

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Approximation of $\mathcal H^2$ functions by bounded ones

Published on 28 Mar 2026 - 13:59

905

Views

Show that the cylindrical $\sigma$-algebra can be written into a countable union of some $\sigma$-algebra

Published on 13 Feb 2020 - 16:47

105

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Solve following SDE

Published on 31 Mar 2026 - 7:14

176

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Confusion about $\ dW_t^2 $ and $\ dt^2$

Published on 27 Mar 2026 - 20:54

134

Views

When does the uniqueness of regular conditional probabilities hold?

Published on 28 Mar 2026 - 13:59

80

Views

What is the joint distribution of $W_t$ and $\int_0^t W_s \,ds$?

Published on 14 Feb 2020 - 13:06

95

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Why does $d(X_tY_t)=X_tdY_t+Y_tdX_t+dX_tdY_t$ hold for Ito process?

Published on 14 Feb 2020 - 15:24

43

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Spectral representation of complex non-negative definite function

Published on 28 Mar 2026 - 6:59

372

Views

Whether two one-dimensional Brownian motions yield a two-dimensional Brownian motion

Published on 28 Mar 2026 - 15:36

List Question

Is it true that $\int_0^t W_s ds = tW_t?$

Expectation of Brownian hitting time

Expectation involving local time of Brownian motion

Local times in higher dimensions

Prove $E\left[\exp^{ia\int_0^Tf(t) \, dB_t}\right]=\exp\left(-\frac{a^2}{2}\int_0^Tf^2(t) \, dt\right)$

Existence of optional quadratic variation (or quadratic co-variation) [X,Y]

Approximation of $\mathcal H^2$ functions by bounded ones

Show that the cylindrical $\sigma$-algebra can be written into a countable union of some $\sigma$-algebra

Solve following SDE

Confusion about $\ dW_t^2 $ and $\ dt^2$

When does the uniqueness of regular conditional probabilities hold?

What is the joint distribution of $W_t$ and $\int_0^t W_s \,ds$?

Why does $d(X_tY_t)=X_tdY_t+Y_tdX_t+dX_tdY_t$ hold for Ito process?

Spectral representation of complex non-negative definite function

Whether two one-dimensional Brownian motions yield a two-dimensional Brownian motion

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