Related papers: Mean Exit Time and Survival Probability within the…

Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…

It is shown in this paper that the quantum master equation can be mapped to a modified continuous time random walk (CTRW) if the relaxation term is composed of transitions over a set of states. When the Hamiltonian is time-independent and…

We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical.…

Epidemiological models help policymakers mitigate disease spread by predicting transmission metrics based on disease dynamics and contact networks. Calibrating these models requires representative network sampling. We investigate the Random…

Random walks have wide application in real lives, ranging from target search, reaction kinetics, polymer chains, to the forecast of the arrive time of extreme events, diseases or opinions. In this paper, we consider discrete random walks on…

This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily…

This paper presents and derives the interrelations between survival analysis and master equation. Survival analysis deals with modeling the transitions between succeeding states of a system in terms of hazard rates. Questions related with…

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 use maximal entropy random walk (MERW) to study the trapping problem in dendrimers modeled by Cayley trees with a deep trap fixed at the central node. We derive an explicit expression for the mean first passage time from any node to the…

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…

Extreme weather events have significant consequences, dominating the impact of climate on society. While high-resolution weather models can forecast many types of extreme events on synoptic timescales, long-term climatological risk…

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we…

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…

We investigate aging continuous time random walks (ACTRW), introduced by Monthus and Bouchaud [{\em J. Phys. A} {\bf 29}, 3847 (1996)]. Statistical behaviors of the displacement of the random walker ${\bf r}={\bf r}(t) - {\bf r}(0)$ in the…

This paper proceeds an approximate calculation of ultimate time survival probability for bi-seasonal discrete time risk model when premium rate equals two. The same model with income rate equal to one was investigated in 2014 by Damarackas…

The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The…

Risk sensitive decision making finds important applications in current day use cases. Existing risk measures consider a single or finite collection of random variables, which do not account for the asymptotic behaviour of underlying…

We present a graph random walk (GRW) method for the study of charge transport properties of complex molecular materials in the time-of-flight regime. The molecules forming the material are represented by the vertices of a directed weighted…

Continuous Time Random Maxima (CTRM) are a generalization of classical extreme value theory: Instead of observing random events at regular intervals in time, the waiting times between the events are also random variables with arbitrary…

The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to…