Monday, January 7, 2019

Ito's Lemma - Integrand depends on upper limit of integration


A problem I came across while practicing using Ito's Lemma had a process with an integral whose integrand depends on the upper limit of integration (the goal is to find $dZ_{t}$):


$Z_{t}=\int_{0}^{t}e^{\frac{t-s}{2}}\sin(B_{s})dB_{s}$, where $B$ is a standard Brownian motion


In what way do I need to take this into account in my solving the problem, if at all?




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