Question

Why is the expectation value of a stochastic integral equal to $\sum_k (\tau_k - t_k)$ where $\tau_k$ denotes the partitioning points?

score 46 · Answer 1 · 2026-03-26 04:35:07

46

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Why is the expectation value of a stochastic integral equal to $\sum_k (\tau_k - t_k)$ where $\tau_k$ denotes the partitioning points?

Published on 26 Mar 2026 - 4:35

score 1k · Answer 2 · 2020-01-11 08:02:21

1k

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Solving Stochastic Differential Equation using integrating factor

Published on 11 Jan 2020 - 8:02

score 82 · Answer 3 · 2020-01-11 23:43:43

82

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stochastic differential equation with inverse mean

Published on 11 Jan 2020 - 23:43

score 41 · Answer 4 · 2026-03-27 20:32:24

41

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is $\int_{0}^{t} dB_s = B_t$?

Published on 27 Mar 2026 - 20:32

score 54 · Answer 5 · 2026-03-26 04:34:03

54

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Show that $\left(\phi\left(X_{t}\right)\right)_{t \geq 0}$ is a martingale

Published on 26 Mar 2026 - 4:34

score 685 · Answer 6 · 2020-01-12 18:34:34

685

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Using Ito Calculus to find $\mathbb{E}[U_t]$ if $U_t= \cos(\sigma W_t)$ where $W_t$ is Brownian Motion

Published on 12 Jan 2020 - 18:34

score 106 · Answer 7 · 2020-01-13 00:03:30

106

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Calculate $\int_{-\infty}^{\infty} \cos(a t) e^{-\frac{t^2}{2}}dt$ using $E[U_t]$ where $U_t = cos(\sigma W_t)$ where $W_t$ is Brownian Motion

Published on 13 Jan 2020 - 0:03

score 37 · Answer 8 · 2020-01-13 13:34:45

37

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Random Variable $X$ pairwise independent to Gaussian $Y, Z$ $\implies$ $X$ uncorrelated to $YZ$?

Published on 13 Jan 2020 - 13:34

score 73 · Answer 9 · 2020-01-15 16:10:01

73

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Distribution of $X_t := \int^\sqrt t _0 \sqrt{2u}\; dB_u$

Published on 15 Jan 2020 - 16:10

score 45 · Answer 10 · 2020-01-17 09:35:08

45

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Which semimartingale representation does the process $U_t = 2 + t^2 + \sin(B_t)\;, t \in [0, \infty)$ satisfy?

Published on 17 Jan 2020 - 9:35

score 77 · Answer 11 · 2020-01-18 22:52:14

77

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Evaluating difficult expectation

Published on 18 Jan 2020 - 22:52

score 75 · Answer 12 · 2020-01-19 09:49:51

75

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Stochastic integral is progressive

Published on 19 Jan 2020 - 9:49

score 74 · Answer 13 · 2020-01-21 22:02:42

74

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Why $X_t^θ= B_1(t) \cos θ − B_2(t) \sin θ$ is a martingale?

Published on 21 Jan 2020 - 22:02

score 828 · Answer 14 · 2026-02-23 04:36:27

828

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Local martingale property for stochastic integrals.

Published on 23 Feb 2026 - 4:36

score 71 · Answer 15 · 2020-01-24 10:10:53

71

Views

If $\int_0^t X_sdB_s$ is a martingale, does $\mathbb E[\int_0^t X_s^2ds]<\infty $?

Published on 24 Jan 2020 - 10:10

List Question

Why is the expectation value of a stochastic integral equal to $\sum_k (\tau_k - t_k)$ where $\tau_k$ denotes the partitioning points?

Solving Stochastic Differential Equation using integrating factor

stochastic differential equation with inverse mean

is $\int_{0}^{t} dB_s = B_t$?

Show that $\left(\phi\left(X_{t}\right)\right)_{t \geq 0}$ is a martingale

Using Ito Calculus to find $\mathbb{E}[U_t]$ if $U_t= \cos(\sigma W_t)$ where $W_t$ is Brownian Motion

Calculate $\int_{-\infty}^{\infty} \cos(a t) e^{-\frac{t^2}{2}}dt$ using $E[U_t]$ where $U_t = cos(\sigma W_t)$ where $W_t$ is Brownian Motion

Random Variable $X$ pairwise independent to Gaussian $Y, Z$ $\implies$ $X$ uncorrelated to $YZ$?

Distribution of $X_t := \int^\sqrt t _0 \sqrt{2u}\; dB_u$

Which semimartingale representation does the process $U_t = 2 + t^2 + \sin(B_t)\;, t \in [0, \infty)$ satisfy?

Evaluating difficult expectation

Stochastic integral is progressive

Why $X_t^θ= B_1(t) \cos θ − B_2(t) \sin θ$ is a martingale?

Local martingale property for stochastic integrals.

If $\int_0^t X_sdB_s$ is a martingale, does $\mathbb E[\int_0^t X_s^2ds]<\infty $?

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