Approximation of occupation time functionals
| Autor: | Randolf Altmeyer |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Fractional Brownian motion Stochastic process Probability (math.PR) Process (computing) Mathematics - Statistics Theory Statistics Theory (math.ST) Upper and lower bounds Local time FOS: Mathematics Statistical physics Brownian motion Mathematics - Probability 62M99 60G99 (Primary) 65D32 (Secondary) Mathematics |
| DOI: | 10.48550/arxiv.1706.03418 |
| Popis: | The strong $L^2$-approximation of occupation time functionals is studied with respect to discrete observations of a $d$-dimensional c\`adl\`ag process. Upper bounds on the error are obtained under weak assumptions, generalizing previous results in the literature considerably. The approach relies on regularity for the marginals of the process and applies also to non-Markovian processes, such as fractional Brownian motion. The results are used to approximate occupation times and local times. For Brownian motion, the upper bounds are shown to be sharp up to a log-factor. Comment: Revised and corrected version. Changed title |
| Databáze: | OpenAIRE |
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