Back to Search
Start Over
Modeling the effect of erosion on crop production
- Source :
- Journal of Applied Probability. 24:787-797
- Publication Year :
- 1987
- Publisher :
- Cambridge University Press (CUP), 1987.
-
Abstract
- This paper is concerned with a model for the effect of erosion on crop production. Crop yield in the year n is given by X(n) = YnLn, where is a sequence of strictly positive i.i.d. random variables such that E{Y 1} is a Markov chain with stationary transition probabilities, independent of . When suitably normalized, leads to a martingale which converges to 0 almost everywhere (a.e.) as n → ∞. In addition, for large n, the distribution of Ln is approximately lognormal. The conditional expectations and probabilities of , given the past history of the process, are determined. Finally, the asymptotic behaviour of the total crop yield is discussed. It is established that under certain regularity conditions Sn converges a.e. to a finite-valued random variable S whose Laplace transform can be obtained as the solution of a Volterra-type linear integral equation.
- Subjects :
- Statistics and Probability
Markov chain
Laplace transform
General Mathematics
Mathematical analysis
010102 general mathematics
Conditional expectation
Integral equation
01 natural sciences
Combinatorics
010104 statistics & probability
Log-normal distribution
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
Almost everywhere
0101 mathematics
Statistics, Probability and Uncertainty
Martingale (probability theory)
Random variable
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 24
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....9bd4997c6d77c6ecf0a6ee281297fdd6