A critical assessment of the HK stochastic integral

Escudero Carlos, Universidad Nacional de Educación a Distancia

The Hänggi-Klimontovich (HK) stochastic integral has been quite frequently used in the statistical physics literature in the last decades. In this talk, we will first introduce its definition and main properties, in particular those that have made it popular as a mathematical tool for physical models. In the sequel, we will show that this stochastic integral possesses undesirable pathological properties in a number of physically motivated counterexamples. To conclude, we will demonstrate that the classical Itô integral is free from such pathologies precisely in these physical models. These results summarize those presented in C. Escudero and H. Rojas, Itô versus Hänggi-Klimontovich, arXiv:2309.03654, 2023.

Area: CS29 - Advances in Stochastic Control and System Modeling (Bernardo D'Auria)

Keywords: Stochastic integration, stochastic differential equations, physical modelling

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