380 Results Found

We consider the first-passage time problem for the Feller-type diffusion process, having infinitesimal drift $B_1(x,t)=\alpha \left(t\right)x+\beta \left(t\right)$ and infinitesimal variance $B_2(x,t)=2r\left(t\right)x$, defined in the space state $[0,+\infty )$, with $\alpha \left(t\right)\in \mathbb{R}$, $\beta \left(t\right)>0$, $r\left(t\right)>0$ continuous...

The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the c...

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time-scale for va...

The arrival of tracers at boundaries with defined distances from the origin of their motion in stochastically fluctuating advection processes is investigated. The advection model is a stationary one-dimensional integrated stochastic process with an a...

Fractal scale-free structures are widely observed across a range of natural and synthetic systems, such as biological networks, internet architectures, and social networks, providing broad applications in the management of complex systems and the fac...

Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the ce...

We consider two different time fractional telegrapher’s equations under stochastic resetting. Using the integral decomposition method, we found the probability density functions and the mean squared displacements. In the long-time limit, the sy...

A two-section semiconductor laser can exhibit excitability for certain parameter settings. When used as a photonic spiking neuron, it is relevant to investigate its sensitivity to noise due to, e.g., spontaneous emission. Under excitable conditions,...

In this paper, we revisit level-dependent quasi-birth-death processes with finitely many possible values of the level and phase variables by complementing the work of Gaver, Jacobs, and Latouche (Adv. Appl. Probab. 1984), where the emphasis is upon o...

A central aspect of in vivo experiments with anticancer therapies is the comparison of the effect of different therapies, or doses of the same therapeutic agent, on tumor growth. One of the most popular clinical endpoints is tumor growth delay, which...

Computing the exact mathematical expression for a quantity defined in terms of a first-passage time random variable for a jump-diffusion process is in general very difficult. In this paper, we consider the following inverse problem: can we find a cer...

Let $X\left(t\right)$ be a continuously time-changed Brownian motion starting from a random position $\eta ,S\left(t\right)$ a given continuous, increasing boundary, with $S\left(0\right)\ge 0,$ $P(\eta \ge S(0\left)\right)=1,$ and F an assigned distri...

First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is...

We study the problem of the first passage time through a constant boundary for a jump diffusion process whose infinitesimal generator is a nonlocal Jacobi operator. Due to the lack of analytical results, we address the problem using a discretization...

For the Wiener, Ornstein–Uhlenbeck, and Feller processes, we study the transition probability density functions with an absorbing boundary in the zero state. Particular attention is paid to the proportional cases and to the time-homogeneous cas...

We analyze a discrete-time random walk on the vertices of an unbounded two-dimensional L-lattice. We determine the probability generating function, and we prove the independence of the coordinates. In particular, we find a relation of each component...

We consider the evolution of a finite population constituted by susceptible and infectious individuals and compare several time-inhomogeneous deterministic models with their stochastic counterpart based on finite birth processes. For these processes,...

In this paper, we consider a stochastic diffusion process able to model the interest rate evolving with respect to time and propose a first passage time (FPT) approach through a boundary, defined as the “alert threshold”, in order to eval...

This paper deals with an infective process of type SIS, taking place in a closed population of moderate size that is inspected periodically. Our aim is to study the number of inspections that find the epidemic process still in progress. As the underl...

In this paper, we study g-fractional diffusion on bounded domains in ${\mathbb{R}}^d$ with absorbing boundary conditions. A new general and explicit representation of the solution is obtained. We study the first-passage time distribution, showing the dependence on...

We consider two different time-inhomogeneous diffusion processes useful to model the evolution of a population in a random environment. The first is a Gompertz-type diffusion process with time-dependent growth intensity, carrying capacity and noise i...

First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first...

We study finite-horizon first-passage time and boundary non-crossing probabilities for Gaussian martingales, viewed as continuous local martingales obtained by running Brownian motion on a deterministic variance clock associated with deterministic vo...

Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers t...

Institutional distrust is treated here not as a low value of trust but as a positive social disposition, the settled expectation that formal procedures and official explanations no longer carry their stated public meaning. The paper studies the conso...

Embarked from the practical conditions of small samples in time-invariant and time-variant uncertainties, a complete non-probabilistic analysis procedure containing uncertainty quantification, uncertainty propagation, and reliability evaluation is pr...

The use of the global mean first-passage time (GMFPT) in random walks on networks has been widely explored in the field of statistical physics, both in theory and practical applications. The GMFPT is the estimated interval of time needed to reach a s...

A proposal is made to employ stochastic models, based on diffusion processes, to represent the evolution of the SARS-CoV-2 virus pandemic. Specifically, two diffusion processes are proposed whose mean functions obey multi-sigmoidal Gompertz and Weibu...

In this article, we numerically investigate the effects of noise and heterogeneity on a model of immune–tumor cell interactions. We focus on stochastic dynamics and simulation-based analysis of the time required for tumor elimination. We identi...

The paper develops a coarse-grained framework for computing mean extinction times in multi-metastable systems modeled as one-step continuous-time Markov chains with an absorbing state. At the microscopic level, backward equations on finite corridors...

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that th...

Does square-lattice symmetry determine the search parameters selected by a fractional random walk with resetting? We compare a walk that updates one coordinate per movement with a walk generated by a fractional power of the full square-torus Laplacia...

For a fractionally integrated Brownian motion (FIBM) of order $\alpha \in (0,1],$$X_{\alpha }\left(t\right),$ we investigate the decaying rate of $P({\tau }_S^{\alpha }>t)$ as $t\to +\infty ,$ where ${\tau }_S^{\alpha }=inf\{t>0:X_{\alpha }\left(t\right)\ge S\}$ is the first-passage time (FP...

Tuned mass dampers (TMDs) are commonly used to reduce excessive vibrations in engineering structures. Although their vibration control performance has been widely studied, the reliability of TMD-equipped structures under stochastic excitations has no...

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M, and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (posi...

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic...

General methods to simulate probability density functions and first passage time densities are provided for time-inhomogeneous stochastic diffusion processes obtained via a composition of two Gauss–Markov processes conditioned on the same initial sta...

We consider the problem of the first passage time T of an inhomogeneous geometric Brownian motion through a constant threshold, for which only limited results are available in the literature. In the case of a strong positive drift, we get an approxim...

Diffusion in heterogeneous environments is usually governed by unusual dynamics, exhibiting sub- or superdiffusive scaling depending on the structural complexity and memory effects. In many systems, diffusing particles may alternate between periods o...

Let $\tau \left(x\right)$ be the first time that a jump-diffusion process with positive and negative jumps leaves the interval $(a,b)$. The moment-generating function $M\left(x\right)$ of $\tau \left(x\right)$ satisfies an integro-differential equation (IDE). In the case of exponential jump...

Reliability prediction of aerospace dormant components requires fusing natural-storage observations at the operating temperature with accelerated-storage testing data at elevated temperatures. Existing scalar-weight fusion methods apply a global weig...

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In t...

The state of a machine is modeled as a controlled continuous-time Markov chain. Moreover, the machine is being serviced at random times. The aim is to maximize the time until the machine must be repaired, while taking the maintenance costs into accou...

Cellular receptors on the cell membrane can bind ligand molecules in the extra-cellular medium to form ligand-bound monomers. These interactions ultimately determine the fate of a cell through the resulting intra-cellular signalling cascades. Often,...

We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state j (operating, F, R). Due to a failure, a transition from a...

An Erlang loss system, which is an $M/G/s/s$ queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the system is full when the service time is...

Filtered Poisson processes are used as models in various applications, in particular in statistical hydrology. In this paper, controlled filtered Poisson processes are considered. The aim is to minimize the expected time that the process will spend i...

Let $\left\{X\right(t),t\ge 0\}$ be a one-dimensional jump-diffusion process whose continuous part is either a Wiener, Ornstein–Uhlenbeck, or generalized Bessel process. The process starts at $X\left(0\right)=x\in [-d,d]$. Let $\tau \left(x\right)$ be the first time that $X\left(t\right)=$...

A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk $\{X_n,n=0,1,\dots \}$ in the continuation region $C:=\{1,2,\dots \}$, and the second player seeks to maxim...

Emerging technology cultivation is formulated as a finite-time stochastic reachability problem under a budget-simplex constraint. Novelty potential, implementation feasibility, and industrial embeddedness form a three-state cascade Itô system,...