58 citations · 248 across the 10 of their papers we have counts for
10 papers
Modelling intermittent anomalous diffusion with switching fractional Brownian motion
Michał Balcerek, Agnieszka Wyłomańska, Krzysztof Burnecki +2
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In ad…
Ruin probability for the quota share model with~phase-type distributed claims
Krzysztof Burnecki, Zbigniew Palmowski, Marek Teuerle +1
In this paper, we generalise the results presented in the literature for the ruin probability for the insurer--reinsurer model under a pro-rata reinsurance contract. We consider cl…
Memory-multi-fractional Brownian motion with continuous correlations
Wei Wang, Michal Balcerek, Krzysztof Burnecki +6
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-depe…
Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions
Michał Balcerek, Krzysztof Burnecki, Samudrajit Thapa +2
Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion be…
Testing of fractional Brownian motion in a noisy environment
Michal Balcerek, Krzysztof Burnecki
Fractional Brownian motion (FBM) is the only Gaussian self-similar process with stationary increments. Its increment process, called fractional Gaussian noise, is ergodic and exhib…
Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
Jakub Ślęzak, Krzysztof Burnecki, Ralf Metzler
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance,…
Valuation of contingent convertible catastrophe bonds - the case for equity conversion
Krzysztof Burnecki, Mario Nicoló Giuricich, Zbigniew Palmowski
Within the context of the banking-related literature on contingent convertible bonds, we comprehensively formalise the design and features of a relatively new type of insurance-lin…
Recognition of stable distribution with Levy index alpha close to 2
Krzysztof Burnecki, Agnieszka Wyłomańska, Aleksei Beletskii +2
We address the problem of recognizing alpha-stable Levy distribution with Levy index close to 2 from experimental data. We are interested in the case when the sample size of availa…
Statistical Modeling of Solar Flare Activity from Empirical Time Series of Soft X-ray Solar Emission
A. A. Stanislavsky, K. Burnecki, M. Magdziarz +2
A time series of soft X-ray emission observed on 1974-2007 years (GOES) is analyzed. We show that in the periods of high solar activity 1977-1981, 1988-1992, 1999-2003 the energy s…
Annuities under random rates of interest - revisited
K. Burnecki, A. Marciniuk, A. Weron
In the article we consider accumulated values of annuities-certain with yearly payments with independent random interest rates. We focus on annuities with payments varying in arith…