11 citations · 54 across the 16 of their papers we have counts for
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math-ph2015★ 5 cited
Multiscale functions, Scale dynamics and Applications to partial differential equations
Jacky Cresson, Frédéric Pierret
Modeling phenomena from experimental data, always begin with a \emph{choice of hypothesis} on the observed dynamics such as \emph{determinism}, \emph{randomness}, \emph{derivabilit…
math.PR2015★ 3 cited
Helmholtz theorem for stochastic Hamiltonian systems
Frédéric Pierret
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamilton…
math.NA2015★ 5 cited
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Jacky Cresson, Frédéric Pierret
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inver…