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Basics of Stochastic Processes

In: Introduction to Stochastic Processes Using R

Author

Listed:
  • Sivaprasad Madhira

    (Savitribai Phule Pune University)

  • Shailaja Deshmukh

    (Savitribai Phule Pune University)

Abstract

Stochastic processes are probability models that describe the evolution of systems that evolve randomly in time and hence are useful in modeling a wide variety of phenomena that occur over time. After a brief introduction in Sect. 1, the notions of a stochastic process and its family of finite dimensional distribution functions are defined and illustrated with examples in Sect. 2. These examples provide a good understanding of the Kolmogorov compatibility conditions as well as the four major types of stochastic processes. Section 3 is devoted to a discussion on processes with stationary and independent increments. Apart from the usual results, a characterization of such processes in terms of characteristic functions is also given. A brief discussion on stationary processes is given in Sect. 4. R software is used throughout the book to illustrate the concepts with numerical examples. In order to facilitate an understanding of R codes, a preliminary introduction to the R software is given in Sect. 5 of this chapter.

Suggested Citation

  • Sivaprasad Madhira & Shailaja Deshmukh, 2023. "Basics of Stochastic Processes," Springer Books, in: Introduction to Stochastic Processes Using R, chapter 0, pages 1-30, Springer.
    • Handle: RePEc:spr:sprchp:978-981-99-5601-2_1
    DOI: 10.1007/978-981-99-5601-2_1
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