Conditions on the boundary and parameters that produce ordering in the first passage time distributions of two different diffusion processes are proved making use of comparison theorems for stochastic differential equations. Three applications of interest in stochastic modeling are presented: a sensitivity analysis for diffusion models characterized by means of first passage times, the comparis...

It it shown that the first-order theory of an automatic structure, whose Gaifman graph has bounded degree, is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). Presenting an automatic structure of bounded degree whose theory is hard for 2EXPSPACE, we also prove this result to be optimal. These findings close the gap left open in [14].

It has been known for a long time that for birth-and-death processes started in zero the first passage time of a given level is distributed as a sum of independent exponentially distributed random variables, the parameters of which are the negatives of the eigenvalues of the stopped process. Recently, Diaconis and Miclo have given a probabilistic proof of this fact by constructing a coupling be...

A new method for constructing first-passage-time probability density functions in the case of regular one-dimensional time homogeneous diffusion processes restricted between constant boundaries is proposed. Some diffusion processes of particular interest in neuronal modeling are considered and thoroughly discusses.

We studied the Mean first passage time for the DNA translocation through a narrow pore. We also proved that, for an asymmetric rachet potential, the mean first passage time for the same DNA to translocate through the membrane can be different when passing from the two different ends, even without external potential. We further extended the situation to a more general case, where a periodic chai...

We develop an analytical approach that provides the dependence of the mean first-passage time (MFPT) for random walks on complex networks both on the target connectivity and on the source-target distance. Our approach puts forward two strongly different behaviors depending on the type-compact or non compact-of the random walk. In the case of non compact exploration, we show that the MFPT scales...

Interaction of capital market participants is a complicated dynamic process. A stochastic model is proposed to describe the dynamics to predict short-term stock price behaviors. Independent compound Poisson processes are introduced to describe the occurrences of market orders, limit orders, and cancellations of limit orders, respectively. Based on high-frequency observations of the limit order ...

In standard planar first-passage percolation [11] each pair x and y of nearest-neighbor of Z has an edge connecting them and each edge is equipped with a non-negative random variable (passage time) which may be interpreted as the time it takes for an infection to be transmitted from x to y. We assume these random variables are i.i.d. with a continuous distribution F. The passage time t(γ) for a...

The concept of the ”transient effect” is examined in respect of a ”mean first passage time”. It is demonstrated that the time the fissioning system stays inside the barrier is much larger than suggested by the transient time, and that no enhancement of emission of neutrons over that given by Kramers’ rate formula ought to be considered.

A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return process in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the mo...