... do yourself a favor.... leave the $100 plus stroller at home... those big, usually expensive ones are usually not user friendly on the Disney busses or trams, as they must be completely folded up to get on.
Unless it is a jogging stroller, a truly expensive stroller is seldom big, at least not when folded. A bulky Graco travel system costs half as much as a Mac Techno, and the Techno is far and away the better stroller for a theme park.
When most folks here worry about expensive strollers, they are worrying about full-featured imported umbrella-fold models, most commonly Maclarens, which are usually over $200 at retail in the US.
I always worried about my Mac walking away, so to give myself peace of mind, I locked it so that it would not fold. This method only requires you to lock it up when you arrive at the park, and then leave it locked until you leave that park (except for the train at MK; the Mac is small enough to carry it on.) I used a long-hasp padlock fastened across a fold joint.
Remember that the name of the game when foiling a thief is to make your stuff the less attractive target in the pool; you can most easily do that by making it take more effort to steal yours. Identify the stroller with unique markings that are hard to remove (and for goodness' sake, forget the diaper trick--who would question someone taking a dirty diaper OFF of a stroller? Especially somewhere where there are trash cans every 20 ft.?). Also be sure that your name and a cell # or resort # are on the stroller, preferably in several places; if it is abandoned and turned in, WDW will contact you if they can.
To prevent mistaken identity, go for markings that stand out and actually cause a bit of bother, so that they will be noticed by anyone who attempts to move the stroller. I used a big froth of metallic curling ribbon around one handle; you could see it glinting in the sun, and it fell over your hand when you tried to push the stroller. Another trick is to put a pr. of kids socks over the handles and secure them on with cable ties; cushions the grips and gives you a good marking.
It's my understanding that deliberate theft of high-end strollers is not that common inside the major parks, but is much more common at DTD, where they have been known to disappear from the parking areas outside the restaurants, especially. I believe that it is getting more common every day, everywhere, thanks to EBay.