Summary
Let (P t ) t>0 , (P * t ) t>0 be two measurable submarkovian semigroups on a measurable spaceE which are absolutely continuous and in duality with respect to a σ-finite measure μ. Then we show that there exists a unique measurable function\(p:]0,\infty [ \times E \times E \to \mathop \mathbb{R}\limits^{\_} _ +\) satisfying
A similar result is shown for inhomogeneous transition functions.
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Wittmann, R. Natural densities of Markov transition probabilities. Probab. Th. Rel. Fields 73, 1–10 (1986). https://doi.org/10.1007/BF01845990
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DOI: https://doi.org/10.1007/BF01845990
Keywords
- Stochastic Process
- Probability Theory
- Measurable Function
- Transition Function
- Mathematical Biology