5 papers
Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
MichaÅ Balcerek, Adrian Pacheco-Pozo, Agnieszka WyÅomaÅska +2
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature…
Machine learning models for predicting catastrophe bond coupons using climate data
Julia KoÅczal, MichaÅ Balcerek, Krzysztof Burnecki
In recent years, the growing frequency and severity of natural disasters have increased the need for effective tools to manage catastrophe risk. Catastrophe (CAT) bonds allow the t…
Testing of tempered fractional Brownian motions
Katarzyna Macioszek, Farzad Sabzikar, Krzysztof Burnecki
We propose here a testing methodology based on the autocovariance, detrended moving average, and time-averaged mean-squared displacement statistics for tempered fractional Brownian…
Multifractional Brownian motion with telegraphic, stochastically varying exponent
MichaÅ Balcerek, Samudrajit Thapa, Krzysztof Burnecki +4
The diversity of diffusive systems exhibiting long-range correlations characterized by a stochastically varying Hurst exponent calls for a generic multifractional model. We present…
Two-dimensional Brownian motion with dependent components: turning angle analysis
MichaÅ Balcerek, Adrian Pacheco-Pozo, Agnieszka WyÅomanska +2
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 m…