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arXiv · 2012.03081

Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications

Lourival Lima·Paulo Ruffino·Francys Souza
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Abstract

In this survey we present the near-optimal stochastic control problem according to some recent tools in the literature. In particular, we focus on the approach of a discretization of the noise values instead of the canonical time-discretization. This is the so called {\it skeleton} structure. This allows to obtain an $\epsilon$-optimal control in non-Markovian systems (the main Theorem). A simple example illustrates the technique. The importance of the approach is emphasised in a final section on open problems related to more geometrical framework and discontinuous noise.

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Lourival Lima, Paulo Ruffino, Francys Souza. 2020-12-05. Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications. https://doi.org/10.1140/epjs/s11734-021-00185-y

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