Worked examples of applying Ito's lemma

In most textbooks Ito's lemma is derived (on different levels of technicality depending on the intended audience) and then only the classic examples of Geometric Brownian motion and the Black-Scholes equation are given.

My question
I am looking for references where lots of worked examples of applying Ito's lemma are given in an easy to follow, step by step fashion. Also more advanced cases should be covered.

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I thought this was an interesting example to add. It concerns a "ratio model" of habit (as opposed to a "difference" model of habit). See, for example, Abel (1990, American Economic Review). Let $$x_t = \lambda \int_{-\infty}^t e^{-\lambda(t-s)} c_s ds.$$ (For context, $x_t$ is a log habit index that is given by a geometric average of past consumption, where $c_t$ is log consumption.) Then by Ito's formula, \begin{align} d x_t &= \lambda \int_{-\infty}^t -\lambda e^{-\lambda(t-s)} c_s ds + \lambda c_t dt \\ &= \lambda (c_t - x_t) dt. \end{align} The part that is interesting to me is the that it easy to err in thinking that the answer is $dx_t = \lambda c_t dt$ or $d x_t = -\lambda x_t dt$.