Sandwiched Processes Driven by Hölder Noises

Giulia Di Nunno (), Yuliya Mishura () and Anton Yurchenko-Tytarenko ()
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Giulia Di Nunno: University of Oslo, Department of Mathematics
Yuliya Mishura: Taras Shevchenko National University of Kyiv, Department of Probability Theory, Statistics and Actuarial Mathematics
Anton Yurchenko-Tytarenko: Statkraft Energi aS

Chapter 3 in Volterra Volatility Models, 2026, pp 79-119 from Springer

Abstract: Abstract This chapter develops the theoretical foundation for a new class of volatility models inspired by the repelling drift behavior of the CIR process discussed in Chap. 2 . We introduce a general stochastic integro-differential equation driven by a general locally Hölder-continuous noise. The defining feature of the model is an explosive drift term that enforces lower (and potentially upper) bounds on the solution—hence the name sandwiched process.

Date: 2026
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DOI: 10.1007/978-3-032-26576-0_3

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