Wiener–Hopf factorization for arithmetic Brownian motion with time-dependent drift and volatility.

In this paper we obtain a Wiener–Hopf type factorization for a real-valued arithmetic Brownian motion with time-dependent drift and volatility. To the best of our knowledge, this paper is the very first step towards realizing the objective of deriving Wiener–Hopf type factorizations for (real-valued) time-inhomogeneous Lévy processes. In order to prove our main theorem, we derive some new results regarding time-inhomogeneous noisy Wiener–Hopf factorization. We demonstrate that in the special case of the arithmetic Brownian motion with constant drift and volatility our main result agrees with classical Wiener–Hopf factorization for this particular time-homogenous Lévy process. [ABSTRACT FROM AUTHOR]