How can I show that the sum of two martingales is a martingale? [closed]
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If I have X and Y, two martingales in the same filtered environment, and a and b two constants, how can I show that :
{aXt + bYt} is also a martingale?
probability stochastic-calculus martingales
closed as off-topic by Did, John B, KReiser, user10354138, Rebellos Dec 5 at 7:14
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If I have X and Y, two martingales in the same filtered environment, and a and b two constants, how can I show that :
{aXt + bYt} is also a martingale?
probability stochastic-calculus martingales
closed as off-topic by Did, John B, KReiser, user10354138, Rebellos Dec 5 at 7:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, John B, KReiser, user10354138, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05
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up vote
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down vote
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If I have X and Y, two martingales in the same filtered environment, and a and b two constants, how can I show that :
{aXt + bYt} is also a martingale?
probability stochastic-calculus martingales
If I have X and Y, two martingales in the same filtered environment, and a and b two constants, how can I show that :
{aXt + bYt} is also a martingale?
probability stochastic-calculus martingales
probability stochastic-calculus martingales
asked Nov 22 at 17:59
Chuck
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closed as off-topic by Did, John B, KReiser, user10354138, Rebellos Dec 5 at 7:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, John B, KReiser, user10354138, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Did, John B, KReiser, user10354138, Rebellos Dec 5 at 7:14
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Did, John B, KReiser, user10354138, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05
add a comment |
By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05
By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05
By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05
add a comment |
1 Answer
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$E(aX_{n+1}+bY_{n+1}|mathcal{F}_n)=aE(X_{n+1}|mathcal{F}_n)+bE(Y_{n+1}|mathcal{F}_n)=aX_n+bY_n$
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1 Answer
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1 Answer
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$E(aX_{n+1}+bY_{n+1}|mathcal{F}_n)=aE(X_{n+1}|mathcal{F}_n)+bE(Y_{n+1}|mathcal{F}_n)=aX_n+bY_n$
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$E(aX_{n+1}+bY_{n+1}|mathcal{F}_n)=aE(X_{n+1}|mathcal{F}_n)+bE(Y_{n+1}|mathcal{F}_n)=aX_n+bY_n$
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$E(aX_{n+1}+bY_{n+1}|mathcal{F}_n)=aE(X_{n+1}|mathcal{F}_n)+bE(Y_{n+1}|mathcal{F}_n)=aX_n+bY_n$
$E(aX_{n+1}+bY_{n+1}|mathcal{F}_n)=aE(X_{n+1}|mathcal{F}_n)+bE(Y_{n+1}|mathcal{F}_n)=aX_n+bY_n$
answered Nov 22 at 18:04
John_Wick
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1,199111
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By the linearity of conditional expectation?
– Federico
Nov 22 at 18:05