3 papers
math.PR2024
Strong existence and uniqueness of a calibrated local stochastic volatility model
Scander Mustapha
We study a two-dimensional McKean-Vlasov stochastic differential equation, whose volatility coefficient depends on the conditional distribution of the second component with respect…
math.PR2023
Well-posedness of the supercooled Stefan problem with oscillatory initial conditions
Scander Mustapha, Mykhaylo Shkolnikov
We study the one-phase one-dimensional supercooled Stefan problem with oscillatory initial conditions. In this context, the global existence of so-called physical solutions has bee…
math.AP2020
Trend to equilibrium for granular media equations under non-convex potential and application to log gases
Scander Mustapha
We derive new HWI inequalities for the granular media equation, which external potential and interaction potential are only strictly convex on complementary parts of the sp…