Formula for the Laplace transform of the projection of a distribution on the positive half-line and some of its applications (Q957814)

Laplace transforms are known to be an important tool in the study of probability distributions on a half-line. Applications of the Laplace transform were addressed, for example, in [\textit{W. Feller}, An introduction to probability theory and its applications. Vol. II. New York-London-Sydney: John Wiley and Sons, Inc. XVIII (1966; Zbl 0138.10207), ch.14]. One can also be interested in the part of the distribution concentrated on the positive or negative half-line (in which case this part is called the projection of the distribution on the corresponding half-line). In this paper, the problem arises of determining the corresponding Laplace transform. A Laplace transform formula will make it possible, for example, to find half-moments. The author gives a formula for the Laplace transform of the projection of a distribution on the positive half-line and some of its applications.