This investigation aims at a new construction of anisotropic fractional Brownian random fields by the white noise approach. Moreover, we investigate its distribution and sample properties （stationariness of increments, self-similarity, sample continuity） which will furnish some useful views to future applications.
The S-integral is a generalized integral of Riemann type which is defined in terms of the Thomson＇s local systems. In this note we prove Gronwall-BeUman＇s inequality for the S-integral. As special cases we also obtain Gronwall-Bellman＇s inequalities for the Henstock integral and the BurkiU approximately continuous integral.
The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.
A family of closed subalgebras, indexed by R (the set of real numbers), of the Wick algebra is constructed. Fundamental properties of the family are shown including the increasing property and the right–continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators.
Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.
