Question

Why $\mathbb E[\Phi(X,Y)]=\int\mathbb E[\Phi(x,Y)]\mathbb P\{X\in dx\}=\mathbb E\int \Phi(x,Y)\mathbb P\{X\in dx\}$ is a consequence of this lemma?

score 31 · Answer 1 · 2020-04-29 09:02:48

31

Views

Why $\mathbb E[\Phi(X,Y)]=\int\mathbb E[\Phi(x,Y)]\mathbb P\{X\in dx\}=\mathbb E\int \Phi(x,Y)\mathbb P\{X\in dx\}$ is a consequence of this lemma?

Published on 29 Apr 2020 - 9:02

score 40 · Answer 2 · 2020-04-30 22:04:33

40

Views

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score 44 · Answer 3 · 2026-03-28 15:20:28

44

Views

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score 1.6k · Answer 4 · 2020-05-03 11:24:59

1.6k

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score 175 · Answer 5 · 2026-03-28 07:57:11

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score 44 · Answer 6 · 2026-03-26 04:33:07

44

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score 229 · Answer 7 · 2026-03-27 13:44:36

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score 220 · Answer 8 · 2020-05-05 16:21:35

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score 176 · Answer 9 · 2026-03-29 03:03:56

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score 69 · Answer 10 · 2026-03-28 14:25:56

69

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score 58 · Answer 11 · 2020-05-06 06:49:45

58

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score 172 · Answer 12 · 2026-02-23 01:05:34

172

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215

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score 442 · Answer 14 · 2026-03-28 20:53:51

442

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score 67 · Answer 15 · 2026-03-28 20:52:54

67

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List Question

Why $\mathbb E[\Phi(X,Y)]=\int\mathbb E[\Phi(x,Y)]\mathbb P\{X\in dx\}=\mathbb E\int \Phi(x,Y)\mathbb P\{X\in dx\}$ is a consequence of this lemma?

Augmentation of the process with left-continuous paths

Clarification in the proof of Lemma 7.3.2 of Oksendale's SDE

How can I prove that Ornstein Uhlenbeck process has a stationnary distribution?

Show ergodicity of transformation of ergodic map

Why does the infinitesimal of a poisson process behave as it does in the Ito multiplication table

Itô-Tanaka formula for a cadlag semimartingale (with a jump process)

Girsanov theorem to show that a process is a solution of a certain SDE using measures on $C[0,1]$

Simple proof of special case of Clark-Ocone formula?

Finding an expectation involving the increment of a symmetric random walk

Covariance of two increasing stochastic processes

Commutativity relationship between the Malliavin derivative and the Skorkohod divergence operators.

Justifying "multiplying by a differential" or a random variable in a stochastic differential equation

Doob-Meyer Decomposition for $(W_{t}^{2}-t)^{2}$

Conditional expectation of an integrated GBM

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