Continuous-Time Stochastic Models
Models in which agents can revise their decisions continuously in time have proved fruitful in the analysis of economic problems involving intertemporal choice under uncertainty (cf. Malliaris and Brock 1982). These models frequently produce significantly sharper results than can be derived from their discrete-time counterparts. In the majority of such cases, the dynamics of the underlying system are described by diffusion processes, whose continuous sample paths can be represented by Ito integrals. However, in selected applications, this assumption can be relaxed to include both non-Markov path-dependent processes and Poisson-directed jump processes.
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