Efficient and theoretically stable inverse Laplace estimation

Develop efficient streaming algorithms for approximately stable numerical inversion of Laplace transforms in set streams, with theoretical guarantees sufficient to estimate broader classes of integral-transform statistics.

Background

For a general Bernstein statistic whose Lévy density is not explicitly known, the paper observes that the density can be recovered through inverse Laplace transformation. Although numerical inversion methods such as Bromwich inversion, Post’s formula, and regularization are discussed, the authors state that these approaches do not currently provide the required theoretical guarantees, particularly multiplicative guarantees suitable for streaming estimation.

The paper therefore identifies efficient, streaming-friendly, and approximately stable Laplace inversion as an unresolved direction for extending the framework beyond statistics with explicitly known Lévy densities.