For assured certainty, there really is no substitute (but one) for the long and sometimes arduous work of genealogical research, following the paper trail backward in history, generation by generation, solidly establishing proof of ancestry before moving on the to the next earlier generation.

There is one exception: Y DNA testing. Y chromosomes are passed from father to son, as are surnames, usually. The test is painless, takes about six weeks and can cost from $99 to around $300, depending how exacting you wish the results to be. Family Tree DNA is the largest, has the largest database, so is therefore most likely to provide you with matches. Their website is http://www.familytreedna.com/ Even if you don't find a match, that in itself will tell you where further research would not likely be fruitful. I see it has a goodly sized, 541 member, Walker surname project where you might be likely to find relatives and answers to your questions. http://www.familytreedna.com/public/...s/default.aspx Also, Family Tree DNA often offers discounts to those who join via a surname project.

You might want to be prepared for disappointment, though, if you have your heart set on being descended from Scottish Walkers. http://www.nationaltrustnames.org.uk shows roughly as many in England as in Scotland.

Good luck!