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Sarvesh Ravichandran Iyer is a post doctoral student under Prof. Sandeep Juneja and a member of the SCDLDS since May 2025. He obtained his dual BS-MS degree from IISc in 2018, and his PhD. in 2024 from ISI, Bangalore. He was a visiting faculty in the mathematics department at Ashoka in the academic year 2024-25. His research interests revolve around pure jump Levy processes and their applications.

Abstract: Exponential tilting is a technique in rare event sampling that uses an underlying change of measure in a probability space, making these rare events more likely. It is applied in multiple domains like finance and climate science to aid with the prediction and mitigation of extreme events. Typically, given some number of samples from an unknown distribution, one is required to produce a large number of exponentially twisted samples from these in order to predict the likelihood of such events. We achieve this aim in two steps. First, we reweigh the samples of the original distribution appropriately using a twisted empirical estimator, and subsequently perform diffusion sampling on the output of the estimator, thereby obtaining more twisted samples. We delineate regimes where the empirical estimator performs well, and where it does not : informally, large twists cannot be performed with very few samples, and twisting unbounded distributions is harder than twisting bounded distributions. We also provide theoretical guarantees on the accuracy of diffusion sampling in these regimes.