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Models of imitation and herding behavior often underestimate the role of individualistic actions and assume symmetric boundary conditions. However, real-world systems (e.g., electoral processes) frequently involve asymmetric boundaries. In…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Virtually all the emergent properties of a complex system are rooted in the non-homogeneous nature of the behaviours of its elements and of the interactions among them. However, the fact that heterogeneity and correlations can appear…
We study and develop the stochastic Markov reward model (sMRM), which extends the Markov chain where transition time/reward as modelled as random variables. Techniques are presented to enable computing first-passage time distributions (or…
Systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a Brownian motion (Bm) driven by…
Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first…
A wide class of ``counting'' problems have been studied in Computer Science. Three typical examples are the estimation of - (i) the permanent of an $n\times n$ 0-1 matrix, (ii) the partition function of certain $n-$ particle Statistical…
We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, such as reachability and full linear temporal logic. The main idea is that we monitor each simulation run on the…
We give exact and explicit expressions of mean first-passage times for random walks in a rectangular domain, in both cases of reflecting boundary conditions and periodic boundary conditions. The situations with one or two absorbing targets…
Understanding excitation and charge transfer in disordered media is a significant challenge in chemistry, biophysics and material science. We study two experimentally-relevant measures for carriers transfer in finite-size chains, the…
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength…
We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
We present general methods to exactly calculate mean-first passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and…
The first-passage time (FPT), defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role to quantify the…
We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only…
The paper is largely of a review nature. It considers two main methods used to study stability and obtain appropriate quantitative estimates of perturbations of (inhomogeneous) Markov chains with continuous time and a finite or countable…
The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…
General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…