On stochastic integral representation of stable processes with sample paths in Banach spaces (original) (raw)

Certain path properties of a symmetric a-stable process X(r) = Is h(t, s) d&f(s), to T, are studied in terms of the kernel h. The existence of an appropriate modification of the kernel h enables one to use results from stable measures on Banach spaces in studying X. Bounds for the moments of the norm of sample paths of X are obtained. This yields definite bounds for the moments of a double a-stable integral. Also, necessary and suflicient conditions for the absolute continuity of sample paths of X are given. Along with the above stochastic integral representation of stable processes, the representation of stable random vectors due to R. LePage, M. Woodroofe, and J. Zinn (1981, Ann. Probab. 9, 624632) is extensively used and the relationship between these two representations is discussed.