I'm trying to understand "backward Brownian motion" and how it relates to standard Brownian motion. In this paper, they construct a solution to Burgers Equation (transformed via Cole-Hopf) with additive space-time white noise using a Feynman-Kac representation. Within this Feynman-Kac representation is a
"backward Brownian motion with diffusion coefficient $2\nu$ starting at time $t$ in $x$ and arriving at time $0$ in $y$."
I interpret this visually as if a (1-D) Brownian motion starts at $x \in \mathbb{R}$ at some time $t$ and "goes to the left" (see below for a rough sketch of what I mean) 
Is that how you would interpret this? How do computations differ from those with normal Brownian motion?
I ask because, in the paper linked above, there is a computation that involves computing the expectation (with respect to the probability measure of the backward Brownian motion) of something like $$ \exp\left(\int_0^t \beta_s ds\right)$$ where $\beta_s$ is the BBM at time $s$. This expectation equals $e^{t^3/6}$, which is what you'd get if $\beta$ were a normal BM...