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32 papers · 1 filter
Ratio limit theorem for renewal processes
Mikael Escobar-Bach, Alexandre Popier, Malo Sahin
We consider a renewal process which models a cumulative shock model that fails when the accumulation of shocks up-crosses a certain threshold. The ratio limit properties of the pro…
Stochastic PDEs driven by G-Brownian motion and the associated Backward Doubly Stochastic Differential Equations
Laurent Denis, Jing Zhang
Our aim is to study the well-posedness of quasilinear stochastic partial differential equations driven by G-Brownian motion (GSPDEs for short) and the associated backward doubly st…
How smooth is the drift of the mixed fractional Brownian motion?
Pavel Chigansky, Marina Kleptsyna
The mixed fractional Brownian motion - the sum of independent fractional and standard Brownian motions - is known to be a semimartingale if the Hurst exponent of its fractional…
Malliavin calculcus for a Hawkes process
Alexandre Popier, Laurent Denis, Dorian Cacitti-Holland
We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables t…
Malliavin derivative and sensitivity for optimal liquidation
Alexandre Popier, Laurent Denis, Dorian Cacitti-Holland
We prove that the solution of the backward stochastic differential equation with terminal singularity has a Malliavin derivative, which is the limit of the derivative of the approx…
The support function of the high-dimensional Poisson polytope
Pierre Calka, Benjamin Dadoun
Let be the convex hull of the intersection of the homogeneous Poisson point process of intensity in , , with the Euclidean unit ball $\mathbb{B}^…