Related papers: Explicit moments of decision times for single- and…
Training can improve human decision-making performance. After several training sessions, a person can quickly and accurately complete a task. However, decision-making is always a trade-off between accuracy and response time. Factors such as…
Human decision making behavior is observed with choice-response time data during psychological experiments. Drift-diffusion models of this data consist of a Wiener first-passage time (WFPT) distribution and are described by cognitive…
In this paper, we establish a relationship between the asymptotic form of conditional boundary crossing probabilities and first passage time densities for diffusion processes. Namely, we show that, under broad assumptions, the first…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
When the unconditioned process is a diffusion process $X(t)$ of drift $\mu(x)$ and of diffusion coefficient $D=1/2$, the local time $A(t)= \int_{0}^{t} d\tau \delta(X(\tau)) $ at the origin $x=0$ is one of the most important time-additive…
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
To make decisions organisms often accumulate information across multiple timescales. However, most experimental and modeling studies of decision-making focus on sequences of independent trials. On the other hand, natural environments are…
This paper investigates a financial market where returns depend on an unobservable Gaussian drift process. While the observation of returns yields information about the underlying drift, we also incorporate discrete-time expert opinions as…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
The time it takes the fastest searcher out of $N\gg1$ searchers to find a target determines the timescale of many physical, chemical, and biological processes. This time is called an extreme first passage time (FPT) and is typically much…
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient…
We consider a tracer particle performing a random walk on a two-dimensional lattice in the presence of immobile hard obstacles. Starting from equilibrium, a constant force pulling on the particle is switched on, driving the system to a new…
This article is accepted for publication in the "Annals I.H.P. Prob. & Stat.". We investigate the ballistic behavior of diffusions in random environment. We introduce conditions in the spirit of (T) and (T') of the discrete setting, cf.…
Consider a one dimensional diffusion process on the diffusion interval $I$ originated in $x_0\in I$. Let $a(t)$ and $b(t)$ be two continuous functions of $t$, $t>t_0$ with bounded derivatives and with $a(t)<b(t)$ and $a(t),b(t)\in I$,…
In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated process stopped at the threshold. Our methodology relies on…
Linear diffusion processes serve as canonical continuous-time models for dynamic decision-making under uncertainty. These systems evolve according to drift matrices that specify the instantaneous rates of change in the expected system…
Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit…
Recently a general growth curve including the well known growth equations, such as Malthus, logistic, Bertallanfy, Gompertz, has been studied. We now propose two stochastic formulations of this growth equation. They are obtained starting…