Piecewise homogeneous random walk with a moving boundary
The authors study a random walk with nearest neighbor transitions on a one-dimensional lattice. The walk starts at the origin, as does a dividing line which moves with constant speed, ..gamma.., but the outward transition probabilities rho/sub A/ and rho/sub B/ differ on the right- and left-hand sides of the dividing line. This problem is solved formally by taking advantage of the analytical properties in the complex plane of an added variable generating function, and it is found that rho/sub A/, rho/sub B/ space decomposes into four regions of distinct qualitative properties. The asymptotic probability of the walk being to the right of the moving boundary is obtained explicitly in three of the four regions. However, analysis in the fourth region is a sensitive function of the denominator of the rational fraction ..gamma.., and so they conclude with a number of special cases which can be solved in closed form.
- Research Organization:
- Courant Institute of Mathematical Sciences, New York Univ., New York, NY 10012
- OSTI ID:
- 5789807
- Journal Information:
- SIAM J. Appl. Math.; (United States), Vol. 47:4
- Country of Publication:
- United States
- Language:
- English
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