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Utilizing non-concurrent control data (NCC) in the analysis of late-entering arms in platform trials has recently received considerable attention. While incorporating NCC can lead to increased power and lower sample sizes, it might…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better…
We prove a general result on a relationship between a limit of normalized numbers of interval crossings by a c\`adl\`ag path and an occupation measure associated with this path. Using this result we define local times of fractional Brownian…
A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
We introduce a general framework for deriving effective dynamics from arbitrary time-dependent generators, based on a systematic operator cumulant expansion. Unlike traditional approaches, which typically assume periodic or adiabatic…
The design and structure of generalized predictive control (GPC) are not simple and intuitive. The performance analysis does not deeply analyze how the controller parameters affect the system characteristics and the relationship between the…
In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractional kinetic (GFK) and telegraph-type equations depending by…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process.…
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed…
We consider the discrete time unitary dynamics given by a quantum walk on $\Z^d$ performed by a particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
In this paper, we study the numerical schemes for the two-dimensional Fokker-Planck equation governing the probability density function of the tempered fractional Brownian motion. The main challenges of the numerical schemes come from the…
A model is presented relating the evolution of genomic GC content over time to AT$\rightarrow$GC and GC$\rightarrow$AT mutation rates. By employing It\^o calculus it is shown that if mutation rates in asexually reproducing organisms are…
In recent years a huge interdisciplinary field has emerged which is devoted to the complex dynamics of anomalous transport with long-time memory and non-markovian features. It was found that the framework of fractional calculus and its…