Sieving random iterative function systems
| Autor: | Ilya Molchanov, Alexander Marynych |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Distribution (number theory) perpetuity iteration 01 natural sciences 010104 statistics & probability Bernoulli's principle 510 Mathematics FOS: Mathematics Applied mathematics Almost surely 0101 mathematics Mathematics sieving Spacetime Stochastic process random Lipschitz function infinite Bernoulli convolutions 010102 general mathematics Probability (math.PR) thinning Function (mathematics) Scale invariance scale invariant process Lipschitz continuity Primary: 26A18 60G18 Secondary: 37C40 60H25 60G55 Mathematics - Probability |
| Zdroj: | Bernoulli 27, no. 1 (2021), 34-65 |
| DOI: | 10.48350/152420 |
| Popis: | It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space components, it is possible to construct a scale invariant stochastic process. We study its distribution and paths properties. In particular, we show that it is c\`adl\`ag and has finite total variation. We also provide examples and analyse various properties of particular sieved iterative function systems including perpetuities and infinite Bernoulli convolutions, iterations of maximum, and random continued fractions. Comment: 36 pages, 2 figures; accepted for publication in Bernoulli |
| Databáze: | OpenAIRE |
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