ABSTRACT

For any given function V (t, x) ∈ C1,2(IR+ × IRn; IR+), associated with the stochastic differential equation 66.1, we define the differential operator L as follows ( [8]):

LV = ∂V ∂t

+ ∂V ∂x

f + 1 2 Tr

{ hT

∂x2 h

} . (66.2)

Let τ denote the maximal interval of existence of the solution process x(t) of the system (Equation 66.1). We say that the solution x(t) is regular if P{τ = ∞} = 1.