Probability distribution of the maximum of a smooth temporal signal
arXiv:cond-mat/0606145 · doi:10.1103/PhysRevLett.98.020601
Abstract
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 non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=<X(0)X(t)>.
arXiv commentFinal version (1 major typo corrected; better introduction). Accepted in Phys. Rev. Lett
References in corpus (15)
- Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
- Persistence exponents for fluctuating interfaces
- Nontrivial Exponent for Simple Diffusion
- Persistence in Nonequilibrium Systems
- Global Persistence Exponent for Critical Dynamics
- Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes
- 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
- Coarsening in the q-State Potts Model and the Ising Model with Globally Conserved Magnetization
- Experimental Persistence Probability for Fluctuating Steps
- Non-Markovian Persistence and Nonequilibrium Critical Dynamics
- Measurement of persistence in 1D diffusion
- Analytical results for random walk persistence
- Spatial survival probability for one-dimensional fluctuating interfaces in the steady state
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- Zero-Crossing Statistics for Non-Markovian Time Series
- From Markovian to non-Markovian persistence exponents
- Effective computations of joint excursion times for stationary Gaussian processes
- A simple method to calculate first-passage time densities of non-smooth processes