On the integral representation of functionals of ltd processest

Abstract

If z is the unique solution of the Itô equation

and if L is a differentiable functional of the (continuous trajectories of z, then we show that

where μ _z is the function of bounded variation corresponding to the derivative of L(z), where ø is the fundamental matrix solutiion ogf the linearized version of the zbove Itô equation, and where is the algebra generated by w(s),s≦t.

^†This work was supported by the national Research Council of canada under Grant A8051.

^†This work was supported by the national Research Council of canada under Grant A8051.

Notes

^†This work was supported by the national Research Council of canada under Grant A8051.