相关论文: Order 1 autoregressive process of finite length
We consider high-order stochastic processes $x(t)$ described by the Langevin equation $\frac{{{d^m}x\left( t \right)}}{{d{t^m}}}= \sqrt{2D} \xi(t)$, where $\xi(t)$ is a delta-correlated Gaussian noise with zero mean, and $D$ is the strength…
The aim of this paper is to investigate how the correlation properties of a stationary Markovian stochastic processes affect the First Passage Time distribution. First Passage Time issues are a classical topic in stochastic processes…
The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
Extreme value functionals of stochastic processes are inverse functionals of the first passage time -- a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Persistence, defined as the probability that a fluctuating signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. It quantifies the kinetics of processes as varied as phase…
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
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…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
In this paper we introduce a modified version of a gaussian standard first-order autoregressive process where we allow for a dependence structure between the state variable $Y_{t-1}$ and the next innovation $\xi_t$. We call this model…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that 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…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
Many natural and physical processes display long memory and extreme events. In these systems, the measured time series is invariably contaminated by noise. As the extreme events display large deviation from the mean behaviour, the noise…
A quantity of interest to characterise continuous-valued stochastic processes is the differential entropy rate. The rate of convergence of many properties of LRD processes is slower than might be expected, based on the intuition for…
In this paper we consider the problem of a measure that allows us to describe the spatial and temporal dependence structure of multivariate time series with innovations having infinite variance. By using recent results obtained in the…