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It's the integral of the final term, ie. after the second plus sign. Recall that the integral of e^-at is (1/a)(1-e^-at)
Exactly, it really is quite obvious.
It's the integral of the final term, ie. after the second plus sign. Recall that the integral of e^-at is (1/a)(1-e^-at)
It's the integral of the final term, ie. after the second plus sign. Recall that the integral of e^-at is (1/a)(1-e^-at)
For clarity, Wu is a Wiener process.
In the first line extend the upper limit of the integral to infinity and replace the integrand with exp[-a(t-u)]H(t-u), where H is the Heaviside function. Then integrate your expression and interchange the order of integration on the final term (valid application of Fubini's theorem since the integrand is absolutely integrable with respect to the product measure dt dW(u)). This will yield the result after a couple of lines of computation.
In the first line extend the upper limit of the integral to infinity and replace the integrand with exp[-a(t-u)]H(t-u), where H is the Heaviside function. Then integrate your expression and interchange the order of integration on the final term (valid application of Fubini's theorem since the integrand is absolutely integrable with respect to the product measure dt dW(u)). This will yield the result after a couple of lines of computation.
Potato.
But what does it mean
I did A-level maths. I failed itI did A level maths in 6th form ( im 44 now ) and 1 look at all that and i realize that i am not able to remember a damn thing............. 3 years wasted
I did degree level maths, and I'm younger than ya, I also can't remember it! Sad timesI did A level maths in 6th form ( im 44 now ) and 1 look at all that and i realize that i am not able to remember a damn thing............. 3 years wasted