Sample path properties of stochastic integrals, and stochastic differentiation

Abstract

Let B be a Brownian motion, and X = H.B be a stochastic integral of B. We give conditions on the smoothness of the process H which imply that if Ms a singular point of the sample path of B (ω) (such as a local maximum, a slow point, or a fast point) then t is also a singular point of X (ω). In the final section we give an application to stochastic differential equations

Keywords:

• Stochastic integral
• sample path
• singular point
• stochastic differential equation

^*Research partially supported by N.S.E.R.C. of Canada.

^*Research partially supported by N.S.E.R.C. of Canada.

Notes

^*Research partially supported by N.S.E.R.C. of Canada.