Chapter 13. Stochastic Dynamical Systems
In this chapter, we will cover the following topics:
- Simulating a discrete-time Markov chain
- Simulating a Poisson process
- Simulating a Brownian motion
- Simulating a stochastic differential equation
Introduction
Stochastic dynamical systems are dynamical systems subjected to the effect of noise. The randomness brought by the noise takes into account the variability observed in real-world phenomena. For example, the evolution of a share price typically exhibits long-term behaviors along with faster, smaller-amplitude oscillations, reflecting day-to-day or hour-to-hour variations.
Applications of stochastic systems to data science include methods for statistical inference (such as Markov chain Monte Carlo) and stochastic ...
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