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Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes

  • Mircea Dan Grigoriu EMAIL logo
Veröffentlicht/Copyright: 25. Mai 2023
Monte Carlo Methods and Applications
Aus der Zeitschrift Monte Carlo Methods and Applications Band 29 Heft 2

Abstract

Finite-dimensional (FD) models X d ⁢ ( t ) , i.e., deterministic functions of time and finite sets of 𝑑 random variables, are constructed for stationary and nonstationary Gaussian processes X ⁢ ( t ) with continuous samples defined on a bounded time interval [ 0 , τ ] . The basis functions of these FD models are finite sets of eigenfunctions of the correlation functions of X ⁢ ( t ) and of trigonometric functions. Numerical illustrations are presented for a stationary Gaussian process X ⁢ ( t ) with exponential correlation function and a nonstationary version of this process obtained by time distortion. It was found that the FD models are consistent with the theoretical results in the sense that their samples approach the target samples as the stochastic dimension is increased.

Keywords: Convergence in functional spaces; basis functions; extremes of random processes; Gaussian processes; Monte Carlo simulation
MSC 2010: 60E05; 60G15; 65C05; 65C20

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Received: 2022-10-28
Revised: 2023-04-04
Accepted: 2023-04-24
Published Online: 2023-05-25
Published in Print: 2023-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods
  3. Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes
  4. Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation
  5. A Metropolis random walk algorithm to estimate a lower bound of the star discrepancy
  6. Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation
https://doi.org/10.1515/mcma-2023-2006
Schlagwörter für diesen Artikel
Convergence in functional spaces; basis functions; extremes of random processes; Gaussian processes; Monte Carlo simulation

Artikel in diesem Heft

  1. Frontmatter
  2. A time-step-robust algorithm to compute particle trajectories in 3-D unstructured meshes for Lagrangian stochastic methods
  3. Monte Carlo estimates of extremes of stationary/nonstationary Gaussian processes
  4. Two stochastic algorithms for solving elastostatics problems governed by the Lamé equation
  5. A Metropolis random walk algorithm to estimate a lower bound of the star discrepancy
  6. Linking the Monte Carlo radiative transfer algorithm to the radiative transfer equation
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