Abstract
The paper presents, a new large deviations principles (SLDP) of non-Freidlin-Wentzell type,
corresponding to the solutions Colombeau-Ito’s SDE. Using SLDP we present a new approach to
construct the Bellman function ????(????, ????) and optimal control ????(????, ????) directly by way of using strong large
deviations principle for the solutions Colombeau-Ito’s SDE. As important application such SLDP, the
generic imperfect dynamic models of air-to-surface missiles are given in addition to the related simple
guidance law. A four, examples have been illustrated proposed approach and corresponding numerical
simulations have been illustrated and analyzed. Using SLDP approach, Jumps phenomena, in financial
markets, also is considered. Jumps phenomena, in financial markets is explained from the first
principles, without any reference to Poisson jump process. In contrast with a phenomenological approach
we explain such jumps phenomena from the first principles, without any reference to Poisson jump
process