Numerical analysis of degenerate Kolmogorov equations of constrained stochastic Hamiltonian systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)2719-2733
Journal / PublicationComputers and Mathematics with Applications
Issue number8
Online published13 May 2019
Publication statusPublished - 15 Oct 2019
Externally publishedYes


In this work, we propose a method to compute numerical approximations of the invariant measures and Rice's formula (frequency of threshold crossings) for a certain type of stochastic Hamiltonian system constrained by an obstacle and subjected to white or colored noise. As an alternative to probabilistic Monte-Carlo simulations, our approach relies on solving a class of degenerate partial differential equations with non-local Dirichlet boundary conditions, as derived in Mertz et al. (2018). A functional analysis framework is presented; regularization and approximation by the finite element method is applied; numerical experiments on these are performed and show good agreement with probabilistic simulations.

Research Area(s)

  • Constrained stochastic Hamiltonian system, Nonlocal boundary conditions, Partial differential equations, Rice's formula