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Could anyone give me some references where I could find
(a) discrete version(s) of Ito's lemma
(b) a proof how it converges to the continuous form in the limit
(c) its usage within stochastic difference equations
(d) a deduction of a discrete version of the Black Scholes model.

Every little bit of information would help.

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Discrete version of Ito's lemma

Could anyone give me some references where I could find
(a) discrete version(s) of Ito's lemma
(b) a proof how it converges to the continuous form in the limit
(c) its usage within stochastic difference equations
(d) a deduction of a discrete version of the Black Scholes model.

Every little bit of information would help.