Non-Stationary Stochastic Processes Estimation: Vector Stationary Increments, Periodically Stationary Multi-Seasonal Increments (De Gruyter Textbook)

Book Details:

• Author: Maksym Luz

• Publisher: de Gruyter

• Binding: Perfect

• Number of Pages: 310

• ISBN-13: 9783111325330

• Languages: English

• Dimensions: 9.6 x 6.7 x 0.6 inches

About The Book:
In an increasingly data-driven world, the ability to forecast future values of economic and physical processes and restore lost information is more crucial than ever. Estimation of Stochastic Processes: Mean Square Optimal Estimation by Maksym Luz addresses the challenge of forecasting, signal cleaning, and noise removal through a deep exploration of stochastic process estimation.

This book focuses on two key factors in stochastic processes estimation:

1. Model Construction: Creating accurate models for the processes under investigation.

2. Available Information: Utilizing information about the structure of these processes to make informed predictions.

Luz investigates mean square optimal estimation—covering extrapolation, interpolation, and filtering of linear functionals dependent on unobserved values in stochastic sequences and processes. The book specifically delves into processes with periodically stationary and long-memory multiplicative seasonal increments, providing a robust framework for handling complex real-world problems.

Key features of the book include:

• Derivation of formulas for calculating the mean square errors and spectral characteristics of optimal estimates.

• A detailed exploration of spectral certainty, where the spectral structure of sequences is exactly known.

• Application of the minimax-robust estimation method when spectral densities are not precisely known, but admissible spectral densities are given.

This text is essential for researchers, practitioners, and students in applied mathematics, economics, and engineering, offering valuable methods for handling real-world stochastic processes and data prediction problems.