Abstract
This paper is concerned with the continuity and differentiability properties of the sample functions of shot processes. A knowledge of these properties is required in applications where it is desired to apply classical analysis techniques to the individual sample functions of the process. Sufficient conditions are given for the sample functions to be continuous and to be continuously differentiable, and it is shown that these conditions are often satisfied in practice. The proofs are based on a new bound for the probability of large deviations of the process. This bound is not limited to the study of sample function properties but is applicable to a variety of problems in which the behavior of the distribution is of interest.
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