stochastic-differential-equations

Chaotic mixing and the statistical properties of scalar turbulence

Sam Punshon-Smith / 2023-04-10

Passive scalar turbulence is the study of how a scalar quantity, such as temperature or salinity, is transported by an incompressible fluid. This process is modeled by the advection diffusion equation \[\begin{equation} \partial_tg_t + u_t\cdot\nabla g_t - \kappa \Delta g_t =…

financial-mathematics

Log-modulated rough stochastic volatility models

Christian Bayer, Fabian Harang and Paolo Pigato / 2023-03-14

New insights about the regularity of the instantaneous variance obtained from realized variance data (see Gatheral, Jaisson, and Rosenbaum (2018), Bennedsen, Lunde, and Pakkanen (2021, to appear) and Fukasawa, Takabatake, and Westphal (2019)), have inspired the development of so-called rough…