Stochastic processes by convolution of noise with smoothing kernels, where the driving noise is a Lévy subordinator.
Why would we want this? One reason is that this gives us a way to create nonparametric distributions over measures.
References
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Walker, Stephen G., Paul Damien, PuruShottam W. Laud, and Adrian F. M. Smith. 1999. “Bayesian Nonparametric Inference for Random Distributions and Related Functions.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 (3): 485–527. https://doi.org/10.1111/1467-9868.00190.
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Wolpert, Robert L. 2006. “Stationary Gamma Processes,” 13.
Wolpert, Robert L., and Katja Ickstadt. 1998. “Simulation of Lévy Random Fields.” In Practical Nonparametric and Semiparametric Bayesian Statistics, edited by Dipak Dey, Peter Müller, and Debajyoti Sinha, 227–42. Lecture Notes in Statistics. New York, NY: Springer. https://doi.org/10.1007/978-1-4612-1732-9_12.
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