Related papers: First detection of threshold crossing events under…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
We study the problem of coincidence detection in time series data, where we aim to determine whether the appearance of simultaneous or near-simultaneous events in two time series is indicative of some shared underlying signal or…
We address some inverse problems for the first-passage place and the first-passage time of a one-dimensional diffusion process $\mathcal X(t)$ with stochastic resetting, starting from an initial position $\mathcal X(0)= \eta ;$ this type of…
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean…
First-passage processes are pervasive across numerous scientific fields, yet a general framework for understanding their response to external perturbations remains elusive. While the fluctuation-dissipation theorem offers a complete linear…
Fractal phenomena may be widely observed in a great number of complex systems. In this paper, we revisit the well-known Vicsek fractal, and study some of its structural properties for purpose of understanding how the underlying topology…
In this paper we present a comprehensive analysis of the solution of the classical problem of finding the distribution density of a random variable - the first passage time to a given domain by the trajectory of a $p$-adic Markov stochastic…
Distributed sensor networks are commonly operated through coincidence logic: if detector reports overlap within a prescribed time window, an event is declared. While effective for clean, high-significance signals, this approach becomes…
Motivated by the Internet-of-things and sensor networks for cyberphysical systems, the problem of dynamic sensor activation for the centralized tracking of an i.i.d. time-varying process is examined. The tradeoff is between energy…
We study the sum of first passage times along an arbitrary cycle made up of N>2 states of a small physical system. We show that, if the system is at thermodynamic equilibrium, this sum follows the same probability distribution regardless of…
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…
In this paper we consider a robot patrolling problem in which events arrive randomly over time at the vertices of a graph. When an event arrives it remains active for a random amount of time. If that time active exceeds a certain threshold,…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
The distribution of the first-passage time (FPT)$T_a$ for a Brownian particle with drift $\mu$ subject to hitting an absorber at a level $a>0$ is well-known and given by its density $\gamma(t) = \frac{a}{\sqrt{2 \pi t^3} } e^{-\frac{(a-\mu…
We propose a new approximation for the distribution of the time of the first level $u$ crossing by the random process $\homV{s}-cs$, where $\homV{s}$, $s>0$, is compound renewal process and $c>0$. It is competitive with respect to existing…
The mean first-passage time (MFPT) is one standard measure for the reaction time in thermally activated barrier-crossing processes. While the relationship between MFPTs and phenomenological rate coefficients is known for systems that…
This paper concerns the first passage times of Bessel processes to a point on the positive real line. We are interested in the case when the process starts at a position on its right and compute the densities of the distributions of the…
We uncover a duality between relaxation and first passage processes in ergodic reversible Markovian dynamics in both discrete and continuous state-space. The duality exists in the form of a spectral interlacing -- the respective time scales…
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…
We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt…