26 citations · 157 across the 57 of their papers we have counts for
5 papers · 2 filters
Optimal approximation of SDEs on submanifolds: the Ito-vector and Ito-jet projections
John Armstrong, Damiano Brigo
We define two new notions of projection of a stochastic differential equation (SDE) onto a submanifold: the Ito-vector and Ito-jet projections. This allows one to systematically de…
SDEs with uniform distributions: Peacocks, Conic martingales and ergodic uniform diffusions
Damiano Brigo, Monique Jeanblanc, Frederic Vrins
It is known since Kellerer (1972) that for any process that is increasing for the convex order, or "peacock" as in Hirsch et al. 2011, there exist martingales with the same margina…
Optimal approximations of the Fokker-Planck-Kolmogorov equation: projection, maximum likelihood eigenfunctions and Galerkin methods
Damiano Brigo, Giovanni Pistone
We study optimal finite dimensional approximations of the generally infinite-dimensional Fokker-Planck-Kolmogorov (FPK) equation, finding the curve in a given finite-dimensional fa…
Coordinate-free Stochastic Differential Equations as Jets
John Armstrong, Damiano Brigo
We explain how Itô Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms…
Projection based dimensionality reduction for measure valued evolution equations in statistical manifolds
Damiano Brigo, Giovanni Pistone
We propose a dimensionality reduction method for infinite-dimensional measure-valued evolution equations such as the Fokker-Planck partial differential equation or the Kushner-Stra…