The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure

Timothy C. Johnson, Mihail Zervos

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We consider the solvability of the ordinary differential equation (ODE)[image omitted]inside an interval [image omitted], where , b, r are given functions and h is a locally finite measure. This ODE is associated with the Hamilton-Jacobi-Bellman (HJB) equations arising in the study of a wide range of stochastic optimisation problems. These problems are motivated by numerous applications and include optimal stopping, singular stochastic control and impulse stochastic control models in which the state process is given by a one-dimensional It diffusion. Under general conditions, we derive both analytic and probabilistic expressions for the solution to equation (1) that is required by the analysis of the relevant stochastic control models. We also establish a number of properties that are important for applications.

Original languageEnglish
Pages (from-to)363-382
Number of pages20
JournalStochastics: An International Journal of Probability and Stochastic Processes
Volume79
Issue number3-4
DOIs
Publication statusPublished - Jun 2007

Keywords

  • Additive functionals
  • Local time
  • Measure-valued inhomogeneity
  • Optimal stopping
  • Second-order linear ordinary differential equations
  • Singular control

Fingerprint Dive into the research topics of 'The solution to a second order linear ordinary differential equation with a non-homogeneous term that is a measure'. Together they form a unique fingerprint.

  • Cite this