Numerical evaluation of Markov transition probabilities based on the discretized product integral. (English) Zbl 0761.65109
The transition matrix of a time-inhomogeneous Markov process is approximated by a product integral of the intensity matrix where the Taylor expansion is used. Approximation errors are given. Easy numerical examples are considered.
Reviewer: W.Grecksch (Merseburg)
MSC:
| 65C99 | Probabilistic methods, stochastic differential equations |
| 60J05 | Discrete-time Markov processes on general state spaces |
Keywords:
matrix norm; transition matrix; time-inhomogeneous Markov process; product integral; intensity matrix; Taylor expansion; numerical examplesReferences:
| [1] | DOI: 10.1007/978-3-642-80753-4 · doi:10.1007/978-3-642-80753-4 |
| [2] | DOI: 10.1214/aos/1176347865 · Zbl 0718.60087 · doi:10.1214/aos/1176347865 |
| [3] | DOI: 10.1137/1020098 · Zbl 0395.65012 · doi:10.1137/1020098 |
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