On Application of Importance Sampling to Probabilistic Dynamics

1.. Introduction Recently,, researchers inn reliability have stressedd the needd too incorporate inn a usual safety study the dynamic behaviour of a system andd its influence onn the transitions likely to occur inn ann accidental transient.. This feedbackk is quantifiedd by the pr obability densities of being inn a givenn state at a givenn time,, withh givenn values of the phy sical variables.. Let us consider a system behavedd deterministically according too the dynami cs inn state i) (x f dt dx i = from time 0 = t too i t t = ,, where a stochastic transitionn occurs according to Markoviann hypothesis withh intensity i λ (F.E.Labeauu (1996)),, last depending onn the phase variable inn general,, i.e..) (x i i λ λ = .. The system thenn changes its state too j,, inn whichh a similar evolutionn takes place until next transition.. Inn this paper we consider a general way of simulating the behavior of the system by Monte-Carloo methodd using a nn important sampling andd stochastic programming. 2.. Improvingg important samplingg byy stochastic programming Ann applicationn of optimizationn techniques too systems reliability andd safety analysis occurs by twoo ways.. First concerns a best choice of parameters i nn important sampling,, say, too choose optimal parameters for measure change (G.I.. from formulationn of standardd programming problems withh objectives/constr aints related withh modeling of rare events (Uryasevv (1995),, Sakalauskas (2002).. Thus,, let us consider the stochastic optimizationn approachh inn general too extendd general conc ept too probabilistic dynamics.