Martingale Transformations of Brownian Motion with Application to Functional Equations

Abstract

We describe the classes of functions f=(f(x), x∈ R), for which processes f(Wt)-Ef(Wt) and f(Wt)/Ef(Wt) are martingales. We apply these results to give a martingale characterization of general solutions of the quadratic and the D'Alembert functional equations. We study also the time-dependent martingale transformations of a Brownian Motion.

0

Turn this paper into a lesson

ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.

Discussion (0)

Sign in to join the discussion.

Loading comments…