STOCHASTIC COMPLEX INTEGRALS ASSOCIATED WITH
HOMOGENEOUS INDEPENDENTLY SCATTERED RANDOM MEASURES
ON THE LINE
Abstract: Complex integrals associated with homogeneous independently scattered random
measures on the line are discussed. Theorems corresponding to Cauchy’s theorem and the
residue theorem are given. Furthermore, the converse of Cauchy’s theorem is discussed.
2000 AMS Mathematics Subject Classification: Primary: 60E07; Secondary:
Keywords and phrases: Stochastic integral, infinitely divisible distribution, Lévy
process, complex integral.