Abstract
The purpose of this paper is twofold: first, to extend the definition of the stochastic integral for processes with values in Banach spaces; and second, to define the stochastic integral as a genuine integral, with respect to a measure, that is, to provide a general integration theory for vector measures, which, when applied to stochastic processes, yields the stochastic integral along with all its properties. For the reader interested only in scalar stochastic integration, our approach should still be of interest, since it sheds new light on the stochastic integral, enlarges the class of integrable processes and presents new convergence theorems involving the stochastic integral.
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Brooks, J.K., Dinculeanu, N. (1991). Stochastic Integration in Banach Spaces. In: Çinlar, E., Fitzsimmons, P.J., Williams, R.J. (eds) Seminar on Stochastic Processes, 1990. Progress in Probability, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-0562-0_4
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DOI: https://doi.org/10.1007/978-1-4684-0562-0_4
Publisher Name: Birkhäuser, Boston, MA
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