Abstract
It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamicsdx=(fx+gu)dt+hdb(t,a) whereb(t, a) is a fractional Brownian motion of ordera, 0<2a<1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments ofx(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.
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G. Jumarie, French citizen of West Indies, Guadeloupe. DrMth (Fr), Dr Univ (Fr), DrSc Phys (Fr) Ing (Fr). Author of the theories of relative cybernetics (Gordon and Breach), relative information and information of non-random functions (Springer) and complexvalued fractional Brownian motion of ordern (Kluwer-Springer) ±350 papers.
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Jumarie, G. A norandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG). JAMC 19, 19–32 (2005). https://doi.org/10.1007/BF02935786
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DOI: https://doi.org/10.1007/BF02935786