Integration by Parts for Ito Integrals a) Show t t0 s dWs = tWt t0Wt0

Integration by Parts for Itˆo Integrals

a) Show

 t t0 s dWs = tWt − t0Wt0 −

 t t0 Ws ds Hint: Start with the Wiener process Xt = Wt and apply the Itˆo Lemma with the transformation y = g(x,t) := tx.

b) Denote ΔY :=  t t0

 s t0 dWz ds. Show by using

a) that

 t t0

 s t0 dz dWs = ΔWΔt − ΔY .