A norandom variational approach to stochastic linear quadratic Gaussian optimization involving fractional noises (FLQG) |
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Authors: | Guy Jumarie |
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Institution: | 1. Department of Mathematics, University of Quebec at Montreal, Downtown St, P.O. Box 8888, H3C 3P8, Montreal, Qc., Canada
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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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