26 citations · 77 across the 19 of their papers we have counts for
6 papers · 1 filter
Anomalous Recurrence Properties of Markov Chains on Manifolds of Negative Curvature
John Armstrong, Tim King
We present a recurrence-transience classification for discrete-time Markov chains on manifolds with negative curvature. Our classification depends only on geometric quantities asso…
Itô Stochastic differentials
John Armstrong, Andrei Ionescu
We give an infinitesimal meaning to the symbol for a continuous semimartingale at an instant in time . We define a vector space structure on the space of differential…
Projections of SDEs onto Submanifolds
John Armstrong, Damiano Brigo, Emilio Ferrucci
In [ABF19] the authors define three projections of Rd-valued stochastic differential equations (SDEs) onto submanifolds: the Stratonovich, Ito-vector and Ito-jet projections. In th…
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…
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…
Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples
John Armstrong, Damiano Brigo
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method…