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It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…

We study the asymptotic tail probability of the first-passage time over a moving boundary for a random walk conditioned to return to zero, where the increments of the random walk have finite variance. Typically, the asymptotic tail behavior…

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as…

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in…

We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…

Issues of resonance that appear in non-standard random walk models are discussed. The first walk is called repulsive delayed random walk, which is described in the context of a stick balancing experiment. It will be shown that a type of…

First passage models, where corporate assets undergo correlated random walks and a company defaults if its assets fall below a threshold provide an attractive framework for modeling the default process. Typical one year default correlations…

We study the dynamics of a deterministic walk confined in a narrow two-dimensional space randomly filled with point-like targets. At each step, the walker visits the nearest target not previously visited. Complex dynamics is observed at…

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which…

Evaluating the completion time of a random algorithm or a running stochastic process is a valuable tip not only from a purely theoretical, but also pragmatic point of view. In the formal sense, this kind of a task is specified in terms of…

In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…

We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…

We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center of mass persistence of a random walker to the…

We study the behaviour of a sequence of biased random walks X(i), i>=0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the i-th walk is the trace of the (i - 1)-st walk. The sequence of bias vectors…

Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary…

Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper marks the initial stride toward achieving this…

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…

We review some representative results for first-passage problems involving so-called mortal or evanescent walkers, i.e., walkers with a finite lifetime. The mortality constraint plays a key role in the modeling of many real scenarios, as it…