Two-dimensional Brownian motion with dependent components: turning angle analysis
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909529571065856 |
|---|---|
| author | Balcerek, Michał Pacheco-Pozo, Adrian Wyłomanska, Agnieszka Burnecki, Krzysztof Krapf, Diego |
| author_facet | Balcerek, Michał Pacheco-Pozo, Adrian Wyłomanska, Agnieszka Burnecki, Krzysztof Krapf, Diego |
| contents | Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different dimensions as independent components. In this article, we investigate a model of correlated Brownian motion in $\mathbb{R}^2$, where the individual components are not necessarily independent. We explore various statistical properties of the process under consideration, going beyond the conventional analysis of the second moment. Our particular focus lies on investigating the distribution of turning angles. This distribution reveals particularly interesting characteristics for processes with dependent components that are relevant to applications in diverse physical systems. Theoretical considerations are supported by numerical simulations and analysis of two real-world datasets: the financial data of the Dow Jones Industrial Average and the Standard and Poor's 500, and trajectories of polystyrene beads in water. Finally, we show that the model can be readily extended to trajectories with correlations that change over time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06374 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-dimensional Brownian motion with dependent components: turning angle analysis Balcerek, Michał Pacheco-Pozo, Adrian Wyłomanska, Agnieszka Burnecki, Krzysztof Krapf, Diego Statistical Mechanics Probability Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different dimensions as independent components. In this article, we investigate a model of correlated Brownian motion in $\mathbb{R}^2$, where the individual components are not necessarily independent. We explore various statistical properties of the process under consideration, going beyond the conventional analysis of the second moment. Our particular focus lies on investigating the distribution of turning angles. This distribution reveals particularly interesting characteristics for processes with dependent components that are relevant to applications in diverse physical systems. Theoretical considerations are supported by numerical simulations and analysis of two real-world datasets: the financial data of the Dow Jones Industrial Average and the Standard and Poor's 500, and trajectories of polystyrene beads in water. Finally, we show that the model can be readily extended to trajectories with correlations that change over time. |
| title | Two-dimensional Brownian motion with dependent components: turning angle analysis |
| topic | Statistical Mechanics Probability |
| url | https://arxiv.org/abs/2407.06374 |