The Approximate Calculation of Invariant Measures of Diffusions Via finite Difference Approximations to Degenerate Elliptic Partial Differential Equations,
Abstract
If L is the (possibly degenerate) differential generator of a diffusion process whose measures coverage to a unique invariant measure Mu, then formally, the value gamma in LV(x) + k(x) - gamma = 0 is the integral of k(x)Mu(dx). A finite difference approximation is used to solve the differential equation. The coefficients in the finite difference equation are one step transition probabilities for some Markov chain whose (suitable) continuous time interpolations converge weakly to the diffusion. Under reasonable conditions, the inverges weakly to the weak sense density of Mu as the finite difference intervals go to zero. The approximating measure can be taken to be the invariant measure (or Cesaro sum of the n-step transition probabilities for the chain), simply weighted, correspondong to any recurrent state in the approximating chain. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 09, 1974
- Accession Number
- AD0778388
Entities
People
- Chen-fu Yu
- Harold J. Kushner
Organizations
- Brown University