A new comparison theorem for solutions of stochastic differential equations

Abstract

Let Z ₁(t) and Z ₂(t) be solutions of two stochastic differential equations. Then Z ₁(t)≦Z ₂(t) for all t⪋0 a.s. provided certain relations involving the coefficients and intial conditions of the equations hold. the diffusion coefficients are not required toi be the same for both equtions

^†My research was supported in part by the Natural Sciences and Engineering Research Council of Canada. I am grateful to Cornell University for its hospitality while I worked on this material. I am indebted to Professor Y. Ogura for his considerable contributions to this work.

^†My research was supported in part by the Natural Sciences and Engineering Research Council of Canada. I am grateful to Cornell University for its hospitality while I worked on this material. I am indebted to Professor Y. Ogura for his considerable contributions to this work.

Notes

^†My research was supported in part by the Natural Sciences and Engineering Research Council of Canada. I am grateful to Cornell University for its hospitality while I worked on this material. I am indebted to Professor Y. Ogura for his considerable contributions to this work.