Fast solutions for the first-passage distribution of diffusion models with space-time-dependent drift functions and time-dependent boundaries

First Passage Time Distribution for Anomalous Diffusion

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

The first - passage time distribution for the diffusion model with variable drift

23 The Ratcliff diffusion model is now arguably the most widely applied model for response time 24 data. Its major advantage is its description of both response times and the probabilities for 25 correct as well as incorrect responses. The model assumes a Wiener process with drift between 26 two constant absorbing barriers. The first-passage times at the upper and lower boundary 27 describe the...

Time-Dependent Real-Space Renormalization Group Method

In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

Sample-dependent first-passage-time distribution in a disordered medium.

Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well described by the annealed continuous-time random walk. We propose an approximate expression for the first-passage-time (FPT) distribution in a given sample that enables detailed comparison of the two problems. For a system of finite size, the number and spatial arrangement of deep traps y...

Space-time models with time-dependent covariates