Calculus for multiplicative functionals, Itô’s formula and differential equations
The theory of stochasic integrals and stochastic differential equations was established by K Itô [3, 4] (also see ). In past four decade years, Itô’s stochastic analysis has established for itself the central role in modern probability theory. Itô’s theory of stochastic differential equations has been one of the most important tools. However, Itô’s construction of stochastic integrals over Brownian motion possesses an essentially random characterization, and is meaningless for a single Brownian path. The Itô map obtained by solving Itô’s stochastic differential equations is nowhere continuous on the Wiener space.
KeywordsBrownian Motion Stochastic Differential Equation Separable Banach Space Stochastic Integral Wiener Space
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