Levy Searches Based on A Priori Information: The Biased Levy Walk

Searching for objects with unknown locations based on random walks can be optimized when the walkers obey Levy distributions with a critical exponent. We consider the problem of optimizing statistical searches when a priori information, such as location densities, are known. We consider both spatially dependent exponents and biased search directions. For spatially localized target distributions and non-destructive searches, the search is most improved by biasing the search direction.