Related papers: Time-dependent probability density function for pa…
Process mining is a well-established discipline of data analysis focused on the discovery of process models from information systems' event logs. Recently, an emerging subarea of process mining, known as stochastic process discovery, has…
Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
Stochastic processes with random reinforced relocations have been introduced in the physics literature to model animal foraging behaviour. Such a process evolves as a Markov process, except at random relocation times, when it chooses a time…
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise in a superharmonic external potential of the form $U(x)\propto x^{2n}$ ($n\in\mathbb{N}$). When the noise is considered to be external,…
In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme…
Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability…
We consider a change-point detection problem for a simple class of Piecewise Deterministic Markov Processes (PDMPs). A continuous-time PDMP is observed in discrete time and through noise, and the aim is to propose a numerical method to…
Employing molecular dynamics simulations of jammed soft particles, we study microscopic responses of force-chain networks to quasi-static isotropic (de)compressions. We show that not only contacts but also interparticle gaps between the…
The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given…
We analytically investigate the dynamic behavior of an an-isotropic active Brownian particle under various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to…
We consider diffusive motion of a particle performing a random walk with L\'evy distributed jump lengths and subject to resetting mechanism bringing the walker to an initial position at uniformly distributed times. In the limit of infinite…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
We study the first-passage time to the origin of a mortal Brownian particle, with mortality rate $ \mu $, diffusing in one dimension. The particle starts its motion from $ x>0 $ and it is subject to stochastic resetting with constant rate $…
We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
The strategy of stochastic resetting is known to expedite the first passage to a target, in diffusive systems. Consequently, the mean first passage time is minimized at an optimal resetting parameter. With Poisson resetting, vanishing…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of…
Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…