Related papers: Persistence of a Continuous Stochastic Process wit…
For AR(1)-processes $X_n=\rho X_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\in\mathbb{N}}$ is an i.i.d. sequence of random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0,\dots, X_N\ge…
In this paper we consider the persistence properties of random processes in Brownian scenery, which are examples of non-Markovian and non-Gaussian processes. More precisely we study the asymptotic behaviour for large $T$, of the probability…
We consider an arbitrary Gaussian Stationary Process X(T) with known correlator C(T), sampled at discrete times T_n = n \Delta T. The probability that (n+1) consecutive values of X have the same sign decays as P_n \sim \exp(-\theta_D T_n).…
Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…
We study the asymptotic behaviour of the probability that a stochastic process $(Z_t)_{t \geq 0}$ does not exceed a constant barrier up to time $T$ (the so called survival probability) when Z is the composition of two independent processes…
Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the…
We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a…
For the moving average process $X_n=\rho \xi_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\ge -1}$ is an i.i.d. sequence of normally distributed random variables, we study the persistence probabilities…
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
This article deals with the asymptotic behaviour as $t\to +\infty$ of the survival function $P[T > t],$ where $T$ is the first passage time above a non negative level of a random process starting from zero. In many cases of physical…
For many stochastic processes, the probability $S(t)$ of not-having reached a target in unbounded space up to time $t$ follows a slow algebraic decay at long times, $S(t)\sim S_0/t^\theta$. This is typically the case of symmetric compact…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
The paper formulates the concept of persistence of excitation for discrete-time linear switched systems, and provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
The persistence exponent \theta for the global order parameter, M(t), of a system quenched from the disordered phase to its critical point describes the probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time interval…
In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration…
In this article, we consider additive functionals $\zeta_t = \int_0^t f(X_s)\mathrm{d} s$ of a c\`adl\`ag Markov process $(X_t)_{t\geq 0}$ on $\mathbb{R}$. Under some general conditions on the process $(X_t)_{t\geq 0}$ and on the function…