https://doi.org/10.1140/epjs/s11734-021-00185-y
Review
Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications
Mathematics Department, UNICAMP-State University of Campinas, Rua Sérgio Buarque de Holanda, 651, 13083-859, Campinas, Brazil
Received:
27
November
2020
Accepted:
26
May
2021
Published online:
6
June
2021
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 skeleton structure. This allows to obtain an 
-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.
Research supported by CAPES 88882.329064/2019-01. Research partially supported by CNPq 305212/2019-2, FAPESP 2020/04426-6 and 2015/50122-0. Research supported by FAPESP 2017/23003-6.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
