Integrate a random function
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Let 
be a proability. Suppose 
is a random function, i.e. 
is a random variable for all 
. How can we evaluate
be a proability. Suppose is a random function, i.e. is a random variable for all . How can we evaluate
? In particular, we may assume 
, where the variance is a function of t.1 个评论
Bruno Luong
2021-5-25
To me integral of random is not mathematically defined (the function is NOT integrable).
In relation you might take a look of SDE
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Torsten
2021-5-25
0 个投票
Matlab tools can not be used for this problem because the integral is not simply a numerical value, but a random variable itself.
I think a statistics forum is the more appropriate place to ask your question.
5 个评论
Shunan Sheng
2021-5-25
Torsten
2021-5-25
Did you somewhere find a reference where e.g. Monto Carlo simulations are used to solve stochastic integrals ?
I have no experience in this field, but I have big doubts whether the naive approach (discretize the interval [0,T], generate random numbers in the discretization points according to f(t) and use "trapz", e.g. , to approximate the integral for this specific realization) makes sense.
Maybe you can find some references in the internet about "Numerical solution of stochastic integrals", if such numerical methods exist at all.
Shunan Sheng
2021-5-25
Bruno Luong
2021-5-25
You might read this https://en.wikipedia.org/wiki/Wiener_process
Shunan Sheng
2021-5-25
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