4 papers
Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs
Guijin Son, Seungone Kim, Catherine Arnett +73
Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM…
Concentration of the truncated variation of fractional Brownian motions of any Hurst index, their -variations and local times
Witold M. Bednorz, RafaÅ M. Åochowski
We obtain bounds for probabilities of deviations of the truncated variation functional of fractional Brownian motions (fBm) of any Hurst index from their expected val…
The It{ô}-Föllmer formula -- nonstandard cases
W. M. Bednorz, R. M. Åochowski, P. L. Zondi +2
The purpose of this note is to prove the It{ô}-Föllmer formula for the cà dlà g paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partit…
Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)
Phumlani L. Zondi, Darlington Hove, RafaÅ M. Åochowski +1
We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}…