Journal of applied mathematics & informatics
- Volume 19 Issue 1_2
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- Pages.19-32
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- 2005
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- 2734-1194(pISSN)
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- 2234-8417(eISSN)
A NONRANDOM VARIATIONAL APPROACH TO STOCHASTIC LINEAR QUADRATIC GAUSSIAN OPTIMIZATION INVOLVING FRACTIONAL NOISES (FLQG)
Abstract
It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.
Keywords
- Fractional Brownian motion;
- Mittag-Leffler function;
- fractional Taylors's series;
- fractional derivative;
- optimal control;
- math-ematical finance