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Abstract: 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... read more's characterization theorem is
proved as one of the most significant consequences of the Ito formula.
Thesis (M.S.)--Tufts University, 2011.
Submitted to the Dept. of Mathematics.
Advisor: Marjorie Hahn.
Committee: Sabir Umarov.
Keyword: Mathematics.read less
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