| This paper attempts to provide an elementary background for stochastic calculus via construction of the Ito integrals. In addition, the Ito formula, an essential tool in the study of stochastic calculus, is proved in detail for the Brownian integrators. A relatively rough proof of the Ito formula in the case of continuous square integrable martingales is also discussed. Finally, Levy's characterization theorem is proved as one of the most significant consequences of the Ito formula. |
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