Three questions about the expectation of Brownian Motion. [on hold]
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Let W(r) is a standard brownian motion which follows N(0,r).
Then, how to calculate
(1) $E(int^1_0W(r)^3dr)$
(2) $E(int^1_0W(r)dr)^2$
(3) $E(W(1)int^1_0W(r)dr)^2$
For (1), my solution is $E(int^1_0W(r)^3dr)$ = $int^1_0E(W(r)^3)dr$ = $int^1_00dr$ = 0.
But, I cannot get idea about others.
Thanks for your time and consideration.
expected-value
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
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Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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put on hold as too broad by amWhy, user10354138, Trevor Gunn, Cesareo, Chinnapparaj R 2 days ago
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
0
down vote
favorite
Let W(r) is a standard brownian motion which follows N(0,r).
Then, how to calculate
(1) $E(int^1_0W(r)^3dr)$
(2) $E(int^1_0W(r)dr)^2$
(3) $E(W(1)int^1_0W(r)dr)^2$
For (1), my solution is $E(int^1_0W(r)^3dr)$ = $int^1_0E(W(r)^3)dr$ = $int^1_00dr$ = 0.
But, I cannot get idea about others.
Thanks for your time and consideration.
expected-value
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as too broad by amWhy, user10354138, Trevor Gunn, Cesareo, Chinnapparaj R 2 days ago
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let W(r) is a standard brownian motion which follows N(0,r).
Then, how to calculate
(1) $E(int^1_0W(r)^3dr)$
(2) $E(int^1_0W(r)dr)^2$
(3) $E(W(1)int^1_0W(r)dr)^2$
For (1), my solution is $E(int^1_0W(r)^3dr)$ = $int^1_0E(W(r)^3)dr$ = $int^1_00dr$ = 0.
But, I cannot get idea about others.
Thanks for your time and consideration.
expected-value
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let W(r) is a standard brownian motion which follows N(0,r).
Then, how to calculate
(1) $E(int^1_0W(r)^3dr)$
(2) $E(int^1_0W(r)dr)^2$
(3) $E(W(1)int^1_0W(r)dr)^2$
For (1), my solution is $E(int^1_0W(r)^3dr)$ = $int^1_0E(W(r)^3)dr$ = $int^1_00dr$ = 0.
But, I cannot get idea about others.
Thanks for your time and consideration.
expected-value
expected-value
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
asked Nov 16 at 0:48
Kyoung Hoon Lee
1
1
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Kyoung Hoon Lee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as too broad by amWhy, user10354138, Trevor Gunn, Cesareo, Chinnapparaj R 2 days ago
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as too broad by amWhy, user10354138, Trevor Gunn, Cesareo, Chinnapparaj R 2 days ago
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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1 Answer
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Hints: $E(int_0^{1}W(r)dr)^{2}=Eint_0^{1}int_0^{1}W(r)W(s)dr ds=int_0^{1}int_0^{1}min{r,s} drds$ and a similar method gives 3): compute $EW(1)^{2}W(r)W(s)$ and the integrate.
answered 2 days ago
Kavi Rama Murthy
39.7k31749
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hints: $E(int_0^{1}W(r)dr)^{2}=Eint_0^{1}int_0^{1}W(r)W(s)dr ds=int_0^{1}int_0^{1}min{r,s} drds$ and a similar method gives 3): compute $EW(1)^{2}W(r)W(s)$ and the integrate.
answered 2 days ago
Kavi Rama Murthy
39.7k31749
add a comment |
up vote
1
down vote
Hints: $E(int_0^{1}W(r)dr)^{2}=Eint_0^{1}int_0^{1}W(r)W(s)dr ds=int_0^{1}int_0^{1}min{r,s} drds$ and a similar method gives 3): compute $EW(1)^{2}W(r)W(s)$ and the integrate.
answered 2 days ago
Kavi Rama Murthy
39.7k31749
add a comment |
up vote
1
down vote
up vote
1
down vote
Hints: $E(int_0^{1}W(r)dr)^{2}=Eint_0^{1}int_0^{1}W(r)W(s)dr ds=int_0^{1}int_0^{1}min{r,s} drds$ and a similar method gives 3): compute $EW(1)^{2}W(r)W(s)$ and the integrate.
answered 2 days ago
Kavi Rama Murthy
39.7k31749
Hints: $E(int_0^{1}W(r)dr)^{2}=Eint_0^{1}int_0^{1}W(r)W(s)dr ds=int_0^{1}int_0^{1}min{r,s} drds$ and a similar method gives 3): compute $EW(1)^{2}W(r)W(s)$ and the integrate.
answered 2 days ago
Kavi Rama Murthy
39.7k31749
answered 2 days ago
Kavi Rama Murthy
39.7k31749
answered 2 days ago
Kavi Rama Murthy
39.7k31749
answered 2 days ago
Kavi Rama Murthy
39.7k31749
39.7k31749
add a comment |
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