Economist08
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Hi
I just cannot understand the following transformation, where \phi(t) is the displacement of an optimal path using standard calculus of variations. All functions are defined between 0 and T. \phi equals zero at 0 and T. r is some discount rate, e it the Euler number, t is time.
\int^{T}_{0}\theta(y(t))e^{-rt}\int^{t}_{0}\phi(\tau)d\tau]dt
This should be equal to
\int^{T}_{0}\int^{T}_{t}\theta(y(\tau))e^{-r\tau}d\tau]\phi(t)]dt
If anybody knows the answer, I would be very happy to get some help here.
Thanks in advance!
I just cannot understand the following transformation, where \phi(t) is the displacement of an optimal path using standard calculus of variations. All functions are defined between 0 and T. \phi equals zero at 0 and T. r is some discount rate, e it the Euler number, t is time.
\int^{T}_{0}\theta(y(t))e^{-rt}\int^{t}_{0}\phi(\tau)d\tau]dt
This should be equal to
\int^{T}_{0}\int^{T}_{t}\theta(y(\tau))e^{-r\tau}d\tau]\phi(t)]dt
If anybody knows the answer, I would be very happy to get some help here.
Thanks in advance!