Pinned Diffusions and Markov Bridges
| Autor: | Florian Hildebrandt, Sylvie Rœlly |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Pure mathematics Markov chain General Mathematics Gaussian Probability (math.PR) 010102 general mathematics Markov process Interval (mathematics) Space (mathematics) 01 natural sciences 010104 statistics & probability symbols.namesake 60G15 60H10 60J60 FOS: Mathematics symbols Initial value problem Point (geometry) 0101 mathematics Statistics Probability and Uncertainty Diffusion (business) Mathematics - Probability Mathematics |
| Zdroj: | Journal of Theoretical Probability. 33:906-917 |
| ISSN: | 1572-9230 0894-9840 |
| DOI: | 10.1007/s10959-019-00954-5 |
| Popis: | In this article we consider a family of real-valued diffusion processes on the time interval $[0,1]$ indexed by their prescribed initial value $x \in \mathbb{R}$ and another point in space, $y \in \mathbb{R}$. We first present an easy-to-check condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in $y$ at time $t=1$. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an It\^o diffusion? We eventually illustrate our precise answer with several examples. Comment: 12 pages |
| Databáze: | OpenAIRE |
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