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.