707 citations
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84 papers · 1 filter
Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
Michał Balcerek, Adrian Pacheco-Pozo, Agnieszka Wyłomańska +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…
Arcsine laws for Brownian motion with Poissonian resetting
Kacper Taźbierski, Marcin Magdziarz
We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulae for the probability density functions…
Stochastic representation of processes with resetting
Marcin Magdziarz, Kacper Taźbierski
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently termi…
Moments of exponential functionals of Lévy processes on a deterministic horizon -- identities and explicit expressions
Zbigniew Palmowski, Hristo Sariev, Mladen Savov
In this work, we consider moments of exponential functionals of Lévy processes on a deterministic horizon. We derive two convolutional identities regarding these moments. The first…
On the distribution of the product of two continuous random variables with an application to electricity market transactions. Finite and infinite-variance case
Julia Adamska, Łukasz Bielak, Joanna Janczura +1
In this paper we study the distribution of a product of two continuous random variables. We derive formulas for the probability density functions and moments of the products of the…
Archimedes' principle for ideal gas
Krzysztof Burdzy, Jacek Małecki
We prove Archimedes' principle for a macroscopic ball in ideal gas consisting of point particles with non-zero mass. The main result is an asymptotic theorem, as the number of poin…