Application of random processes

Author: Lin Yuanlie
Publisher:
Publish Date: 2004-05-01
Features: This textbook strives to emphasize the following points:
1. Focuses on sparking interest, enabling readers to grasp the ideas and appreciate their charm and power.
2. Emphasizes revealing the origins and backgrounds of concepts, the refinement of typical random models, their characteristic descriptions, application contexts, and the traces of their development.
3. Primarily uses probabilistic perspectives and methods to study and explore the main features and elegance of several fundamental but still vibrant and promising random processes.
4. Treats conditional mathematical expectation as one of the fundamental concepts of modern random processes and strives to describe its definition and important properties in an elementary and intuitively clear manner.
5. Provides preliminary introductions to several rapidly developing branches with increasingly widespread applications, such as martingales, Brownian motion and It? stochastic integrals, and point processes.
6. Highlights the fundamental ideas and techniques embedded in the general formulas, using them as one of the guiding threads of the textbook and elaborates on their clarification and application.
7. Reflects several new achievements, serving as a starting point for combining teaching and research. The content of this book ranges from elementary introductions to modern frontiers, including prerequisite knowledge, Poisson processes, discrete-time Markov chains, discrete martingales, continuous-time Markov chains, stochastic differential equations, and wide-sense stationary processes.