Stochastic Differential Equations

Starting from this chapter, we begin the study of Stochastic Differential Equations, hereafter abbreviated as SDEs. As anticipated in Sect. 2.6 , such equations were originally introduced for the construction of continuous Markov processes or diffusions. Over time, SDEs have become increasingly important in stochastic modeling across a wide range of fields. SDEs generalize deterministic differential equations by incorporating a random perturbation factor, which allows them to model systems that are subject to uncertainty. In addition, SDEs can be used to construct explicit examples of continuous semimartingales.