Related papers: Classical first passage problems for $p$-adic stoc…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
We study the quickest detection problem of a sudden change in the arrival rate of a Poisson process from a known value to an unknown and unobservable value at an unknown and unobservable disorder time. Our objective is to design an alarm…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…
Based on the analysis of probability flow, where the First Passage (FP) is realised as the sink of probability, we summarise the protocol to find the distribution of the First Passage Time (FTP). We also describe the corresponding formula…
Numerous applications all the way from biology and physics to economics depend on the density of first crossings over a boundary. Motivated by the lack of analytical tools for computing first-passage time densities (FPTDs) for complex…
We consider the problem of the distribution of the sojourn time in a compact set $\mathbb{Z}_{p}$ in the case of a $p$-adic random walk. We rely on the results of our previous studies of the distribution of the first return time for a…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Adsorption to a surface, reversible-binding, and trapping are all prevalent scenarios where particles exhibit "stickiness". Escape and first-passage times are known to be drastically affected, but detailed understanding of this phenomenon…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
The goal of this paper is to analyze distributional Markov Decision Processes as a class of control problems in which the objective is to learn policies that steer the distribution of a cumulative reward toward a prescribed target law,…
The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the…
Gated first-passage processes, where completion depends on both hitting a target and satisfying additional constraints, are prevalent across various fields. Despite their significance, analytical solutions to basic problems remain unknown,…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
In this invited contribution, we revisit the stochastic shortest path problem, and show how recent results allow one to improve over the classical solutions: we present algorithms to synthesize strategies with multiple guarantees on the…
In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process,…
An important open problem in the theory of L\'evy flights concerns the analytically tractable formulation of absorbing boundary conditions. Although numerical studies using the correctly defined nonlocal approach have yielded substantial…
First-passage times are often the most relevant aspect of a complex Markovian network, because they signify when information processing has resulted in a definite decision. Previous studies have shown that for kinetic proofreading networks…
We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction…
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…