Persistence in a Stationary Time-series

Abstract

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice.

8 pages revtex

References in corpus (36)

• Discrete scale invariance and complex dimensions
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Persistence exponents for fluctuating interfaces
• Nontrivial Exponent for Simple Diffusion
• Coarsening and persistence in the voter model
• Global Persistence Exponent for Critical Dynamics
• Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes
• Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments
• Survival Probability of a Gaussian Non-Markovian Process: Application to the T=0 Dynamics of the Ising Model
• Spatial Persistence of Fluctuating Interfaces
• Experimental Measurement of the Persistence Exponent of the Planar Ising Model
• Persistence of Kardar-Parisi-Zhang Interfaces
• Large deviations and nontrivial exponents in coarsening systems
• Persistence with Partial Survival
• Kinetics of Heterogeneous Single-Species Annihilation
• Diffusive persistence and the `sign-time' distribution
• Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models
• Proportion of Unaffected Sites in a Reaction-Diffusion Process
• Measurement of persistence in 1D diffusion
• Inelastic collapse of a randomly forced particle
• Fluctuation Kinetics in a Multispecies Reaction-Diffusion System
• Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials
• Persistence of a Continuous Stochastic Process with Discrete-Time Sampling
• Partial survival and inelastic collapse for a randomly accelerated particle
• Analytical results for random walk persistence
• Critical dimensions of the diffusion equation
• Global Persistence in Directed Percolation
• Survival-Time Distribution for Inelastic Collapse
• Survival Probability of a Mobile Particle in a Fluctuating Field
• Unusual Dynamical Scaling in the Spatial Distribution of Persistent Sites in 1D Potts Models
• Persistence distributions for non gaussian markovian processes
• Exponents appearing in heterogeneous reaction-diffusion models in one dimension
• Persistence and Quiescence of Seismicity on Fault Systems
• Persistence exponent of the diffusion equation in epsilon dimensions
• Persistence exponents of non-Gaussian processes in statistical mechanics
• A universality class in Markovian persistence

Cited by in corpus (12)

• Dark Matter and Dark Energy
• Persistence in Complex Systems
• Persistence Exponents and the Statistics of Crossings and Occupation Times for Gaussian Stationary Processes
• Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models
• Persistence of a Continuous Stochastic Process with Discrete-Time Sampling: Non-Markov Processes
• The Statistics of the Number of Minima in a Random Energy Landscape
• Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence
• Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics
• Persistence exponents via perturbation theory: AR(1)-processes
• Persistence of Non-Markovian Gaussian Stationary Processes in Discrete Time
• Records for the moving average of a time series
• Persistence exponents of self-interacting random walks