Article contents
Approximation of Uniform Transport Process on a Finite Interval to Brownian Motion
Published online by Cambridge University Press: 22 January 2016
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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).
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 1968
References
[2]
Ikeda, N., Nagasawa, M. and Watanabe, S.: A construction of Branching Markov process by piecing out. Proc. Japan Acad., Vol. 42 No. 4 (1966), 370–375.Google Scholar
[3]
Ikeda, N., Nagasawa, M. and Watanabe, S.: Foundation of branching Markov processes. Seminar on Prob., Vol. 23 (1966), (Japanese).Google Scholar
[4]
Ikeda, N., Nomoto, H. and others: Various problems in branching Markov precesses. Seminar on Prob., Vol. 25 (1966), (Japanese).Google Scholar
[5]
Trotter, H.F.: Approximation of Semigroups of Operators. Pacific Jour. Math., Vol. 8 (1958), 887–919.Google Scholar
You have
Access
- 12
- Cited by