random walk and pascals triangle

[Scotty2Cues]

Hi,

Im trying to do a bit of theory using a 1 dimensional random walk. Im trying to count the number of paths on Pascals triangle from start to any node eliminating some of the paths (stop loss). I know without restrictions its n!/(n-r)!r! but I cant workout the formula with resrictions on the number of paths. Im basically trying to work out the probability of getting to a node...
any ideas appreciated

thanks

 

[wackypete2]

I think you are referring to a self-avoiding random walk? or loop-erased random walk. You are seriously jogging my memory from my college days (which is clouded by alcohol but that's a different story!) There are some interesting books about the subject that may not be exactly what you are looking for but could be a starting point. You're not likely to find many here that understand P's triangle.

Good Luck!

Peter

 

[Scotty2Cues]

I think you are referring to a self-avoiding random walk? or loop-erased random walk. You are seriously jogging my memory from my college days (which is clouded by alcohol but that's a different story!) There are some interesting books about the subject that may not be exactly what you are looking for but could be a starting point. You're not likely to find many here that understand P's triangle.

Good Luck!

Peter

thanks. Its not self avoiding. Looking for proability of getting to a specifice node (or two) to simulate stop loss and take profit. These nodes are the endpoints of a 1D walk. So I can only visit that node once (provided the other has not been visited) and I cant travel past the nodes (endpoints/boundaries)

I was going to find the probability of reaching it in exactly N steps, N+1 steps, N+2 steps...... and then sum the probabilities using infinite series. I assign a probability to either direction. So Im really looking for the number of ways of getting to a node in exactly N steps with the restriction that I can only visit that node on the last step. I can do it using Pasacals triangle using a simple method but havent been able to get a formula....