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Two-dimensional Brownian motion with dependent components: Turning angle analysis.

Michał Balcerek1,2, Adrian Pacheco-Pozo2, Agnieszka Wyłomańska1

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This summary is machine-generated.

This study introduces a correlated Brownian motion model in two dimensions, revealing unique turning angle distributions for dependent signals. This advances modeling for financial data and physical systems.

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Area of Science:

  • Stochastic processes
  • Statistical physics
  • Financial mathematics

Background:

  • Brownian motion is a fundamental stochastic process used across science and finance.
  • Standard models often assume independent dimensions, limiting applicability to correlated phenomena.
  • Analyzing statistical properties beyond the second moment is crucial for complex systems.

Purpose of the Study:

  • To investigate a novel model of correlated Brownian motion in R2.
  • To explore statistical properties, particularly the distribution of turning angles, in dependent dimensional processes.
  • To demonstrate the model's relevance using financial and physical system data.

Main Methods:

  • Development of a correlated Brownian motion model in two dimensions.
  • Analysis of statistical properties, focusing on turning angle distributions.
  • Validation through numerical simulations and real-world datasets (stock market, particle trajectories).

Main Results:

  • The model captures dependencies between dimensions, unlike traditional independent models.
  • Turning angle distributions exhibit unique characteristics for correlated Brownian motion.
  • The model shows applicability to financial market data and physical particle movement.

Conclusions:

  • Correlated Brownian motion provides a more realistic framework for systems with interdependent components.
  • The turning angle distribution is a key indicator of dimensional dependence.
  • The proposed model is versatile and extendable to time-varying correlations.