Calculating expected value of a complex wiener process (geometric, cosine, quadratic multiplications)
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$$W_t$$ is defined as a wiener process.
How could the expected value of the equation below be calculated on condition that t=1?
$$Y_t = W^2_t * cos^4(W_t) e^{-frac32 W^2_t}.$$
At first, I have attempted to simplify the equation partially by getting rid of the biquadratic term $cos^4(W_t)$ through the $cos(2x)=2cos^2(x)-1$ equation but I am unable to relate and proceed further with the rest of the function terms.
An explanatory solution or help will be greatly appreciated since it is significant for me to find a solution at earliest convenience.
Thank you for your assistance.
stochastic-processes brownian-motion expected-value
edited Nov 13 at 0:16
Fnacool
4,891511
asked Nov 9 at 22:46
ozi
13
add a comment |
up vote
0
down vote
favorite
$$W_t$$ is defined as a wiener process.
How could the expected value of the equation below be calculated on condition that t=1?
$$Y_t = W^2_t * cos^4(W_t) e^{-frac32 W^2_t}.$$
At first, I have attempted to simplify the equation partially by getting rid of the biquadratic term $cos^4(W_t)$ through the $cos(2x)=2cos^2(x)-1$ equation but I am unable to relate and proceed further with the rest of the function terms.
An explanatory solution or help will be greatly appreciated since it is significant for me to find a solution at earliest convenience.
Thank you for your assistance.
stochastic-processes brownian-motion expected-value
edited Nov 13 at 0:16
Fnacool
4,891511
asked Nov 9 at 22:46
ozi
13
Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
$$W_t$$ is defined as a wiener process.
How could the expected value of the equation below be calculated on condition that t=1?
$$Y_t = W^2_t * cos^4(W_t) e^{-frac32 W^2_t}.$$
At first, I have attempted to simplify the equation partially by getting rid of the biquadratic term $cos^4(W_t)$ through the $cos(2x)=2cos^2(x)-1$ equation but I am unable to relate and proceed further with the rest of the function terms.
An explanatory solution or help will be greatly appreciated since it is significant for me to find a solution at earliest convenience.
Thank you for your assistance.
stochastic-processes brownian-motion expected-value
edited Nov 13 at 0:16
Fnacool
4,891511
asked Nov 9 at 22:46
ozi
13
$$W_t$$ is defined as a wiener process.
How could the expected value of the equation below be calculated on condition that t=1?
$$Y_t = W^2_t * cos^4(W_t) e^{-frac32 W^2_t}.$$
At first, I have attempted to simplify the equation partially by getting rid of the biquadratic term $cos^4(W_t)$ through the $cos(2x)=2cos^2(x)-1$ equation but I am unable to relate and proceed further with the rest of the function terms.
An explanatory solution or help will be greatly appreciated since it is significant for me to find a solution at earliest convenience.
Thank you for your assistance.
stochastic-processes brownian-motion expected-value
stochastic-processes brownian-motion expected-value
edited Nov 13 at 0:16
Fnacool
4,891511
asked Nov 9 at 22:46
ozi
13
edited Nov 13 at 0:16
Fnacool
4,891511
asked Nov 9 at 22:46
ozi
13
edited Nov 13 at 0:16
Fnacool
4,891511
edited Nov 13 at 0:16
Fnacool
4,891511
edited Nov 13 at 0:16
Fnacool
4,891511
4,891511
asked Nov 9 at 22:46
ozi
13
asked Nov 9 at 22:46
ozi
13
asked Nov 9 at 22:46
ozi
13
13
Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29
add a comment |
Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29
Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29
add a comment |
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Hello @ozi, welcome tot MSE. If you want to edit your question properly, be sure to use MathJax. How to use MathJax is explained here.
– Ernie060
Nov 9 at 22:59
Thanks for your help @Ernie060.
– ozi
Nov 10 at 17:29