Stochastic integral

Abstract

(g(t, o)-g(t{_l, ,o)) i-'1 + f(ta, w)(g(t, for t t t+, if f(t,) e S(to, tl, ..., t,) this definition is independent of the special choice of S(to, t, ..., t,). We have the Tem 2.1. I(t, af + bg)=aI(t, o ;f)+ bI(t, (o g) I(t, ,o ;1)=g(t, ,o)-g(O,(o), I(t. o ;f) is a continuous function of t with P-measure 1, III(t, ,o ;f)ll)=llf(r, ,o) IIo, tn for any t, 0 t 1, p{,o sup I(t, 0tgl if f(t, ,o)= h(t, ,o), 0 < u