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ON THE CONVOLUTION OF INVERSE GAUSSIAN AND EXPONENTIAL RANDOM VARIABLES

ABSTRACT We consider the open problem of convolving the first-passage time of a Wiener diffusion process with drift μ and variance parameter with an independent exponential random variable with rate λ. We show that if λ is larger than then the convolution density may be represented using the real and complex parts of the complex error function. Potential applications are briefly mentioned.