Integration with respect to fractal functions and stochastic calculus. I
成果类型：
Article
署名作者：
Zahle, M
署名单位：
Friedrich Schiller University of Jena
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s004400050171
发表日期：
1998
页码：
333-374
关键词：
摘要：
The classical Lebesgue-Stieltjes integral integral(a)(b)f dg of real or complex-valued functions on a finite interval (a, b) is extended to a large class of integrands f and integrators g of unbounded variation. The key is to use composition formulas and integration-by-part rules for fractional integrals and Weyl derivatives. In the special case of Holder continuous functions f and g of summed order greater than 1 convergence of the corresponding Riemann-Stieltjes sums is proved. The results are applied to stochastic integrals where g is replaced by the Wiener process and f by adapted as well as anticipating random functions. In the anticipating case we work within Slobodeckij spaces and introduce a stochastic integral for which the classical Ito formula remains valid. Moreover, this approach enables us to derive calculation rules for pathwise defined stochastic integrals with respect to fractional Brownian motion.
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