On stochastic integral representation of stable processes with sample paths in Banach spaces

Certain path properties of a symmetric [alpha]-stable process X(t) = [integral operator]Sh(t, s) dM(s), t [set membership, variant] 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 [alpha]-stable integral. Also, necessary and sufficient 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[13], Ann. Probab.9, 624-632) is extensively used and the relationship between these two representations is discussed.