A walk on the square lattice is a sequence of steps from a given step set, and the length of the walks is the size of the sequence. The enumeration and asymptotics of walks has been of interest, and much progress has been made within the past few decades. We look at a particular weighted family of walks confined to the positive orthant in $d$ dimensions.
We introduce the standard techniques used in manipulating functional equations to extract the desired terms from generating functions. Then we combine results from analytic combinatorics and complex analysis to find asymptotics.