Prove that $limlimits_{n to infty} P(Lambda_n | F_n) = 1_{Lambda}.$
-1
Let be $(F)_{n}$ filtration and $ A_{n} in F_{n}$ for every $n geq 0$. Let be $$ Lambda_{n} = bigcup_{m geq n} A_m $$ and $$Lambda = bigcap_n A_n. $$
Prove that $limlimits_{n to infty} P(Lambda_n | F_n) = 1_{Lambda}.$
Please someone help me, i do not now how to start. Thx.
real-analysis functional-analysis stochastic-processes stochastic-calculus martingales
edited Jan 6 at 17:08
rtybase
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
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add a comment |
-1
Let be $(F)_{n}$ filtration and $ A_{n} in F_{n}$ for every $n geq 0$. Let be $$ Lambda_{n} = bigcup_{m geq n} A_m $$ and $$Lambda = bigcap_n A_n. $$
Prove that $limlimits_{n to infty} P(Lambda_n | F_n) = 1_{Lambda}.$
Please someone help me, i do not now how to start. Thx.
real-analysis functional-analysis stochastic-processes stochastic-calculus martingales
edited Jan 6 at 17:08
rtybase
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09
add a comment |
-1
-1
-1
Let be $(F)_{n}$ filtration and $ A_{n} in F_{n}$ for every $n geq 0$. Let be $$ Lambda_{n} = bigcup_{m geq n} A_m $$ and $$Lambda = bigcap_n A_n. $$
Prove that $limlimits_{n to infty} P(Lambda_n | F_n) = 1_{Lambda}.$
Please someone help me, i do not now how to start. Thx.
real-analysis functional-analysis stochastic-processes stochastic-calculus martingales
edited Jan 6 at 17:08
rtybase
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Let be $(F)_{n}$ filtration and $ A_{n} in F_{n}$ for every $n geq 0$. Let be $$ Lambda_{n} = bigcup_{m geq n} A_m $$ and $$Lambda = bigcap_n A_n. $$
Prove that $limlimits_{n to infty} P(Lambda_n | F_n) = 1_{Lambda}.$
Please someone help me, i do not now how to start. Thx.
real-analysis functional-analysis stochastic-processes stochastic-calculus martingales
real-analysis functional-analysis stochastic-processes stochastic-calculus martingales
edited Jan 6 at 17:08
rtybase
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Jan 6 at 17:08
rtybase
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited Jan 6 at 17:08
rtybase
10.5k21533
edited Jan 6 at 17:08
rtybase
10.5k21533
edited Jan 6 at 17:08
rtybase
10.5k21533
10.5k21533
asked Jan 6 at 16:55
t.krt.kr
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 6 at 16:55
t.krt.kr
11
asked Jan 6 at 16:55
t.krt.kr
11
11
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
t.kr is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09
add a comment |
In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09
In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09
add a comment |
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In which sense the convergence is supposed to hold? Do you know some related results?
– Davide Giraudo
Jan 6 at 21:22
we need to show that it converges on points. i suppose that this exercise belongs to topic martingals.
– t.kr
Jan 7 at 16:05
If it helps: Let be $(Omega, F, P)$ probability space. Filtration is consequence of $sigma$ - algebras on $(Omega, F, P)$.
– t.kr
Jan 7 at 16:09