76 citations · 88 across the 9 of their papers we have counts for
11 papers
A probabilistic representation of the solution to a 1D evolution equation in a medium with negative index
Éric Bonnetier, Pierre Etoré, Miguel Martinez
In this work we investigate a 1D evolution equation involving a divergence form operator where the diffusion coefficient inside the divergence is changing sign, as in models for me…
Stochastic processes associated to multidimensional parabolic transmission problems in divergence form
Pierre Etore, Miguel Martinez
In this note we define and study the stochastic process in link with a parabolic transmission operator in divergence form. The transmission operator involves a diffr…
A transformed stochastic Euler scheme for multidimensional transmission PDE
Pierre Etore, Miguel Martinez
In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix alo…
Time inhomogeneous Stochastic Differential Equations involving the local time of the unknown process, and associated parabolic operators
Pierre Etoré, Miguel Martinez
In this paper we study time-inhomogeneous versions of one-dimensional Stochastic Differential Equations (SDE) involving the Local Time of the unknown process on curves. After provi…
A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton-Jacobi Integrodifferential Systems on Networks
Dan Goreac, Magdalena Kobylanski, Miguel Martinez
We study optimal control problems in infinite horizon when the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (…
Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes
Dan Goreac, Miguel Martinez
We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in term…