Approximation of Uniform Transport Process on a Finite Interval to Brownian Motion
- 1 June 1968
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 32, 297-314
- https://doi.org/10.1017/s0027763000026738
Abstract
Let us consider a finite closed interval [− a, a] which will be thought of as being a medium capable of transporting particles. These particles may move only to the right or to the left with the constant speed c, and each particle changes the moving-direction during the time Δ with probability kΔ + o(Δ). If a right- (left-) moving particle hits the boundary point a (— a), then either it turns to the left (right) with probability 1 — q1(1 − q-1) or dies with probability q1(q-1).Keywords
This publication has 2 references indexed in Scilit:
- A construction of markov processes by piecing outProceedings of the Japan Academy, Series A, Mathematical Sciences, 1966
- Approximation of semi-groups of operatorsPacific Journal of Mathematics, 1958