Modeling the effect of erosion on crop production
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}
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| Veröffentlicht in: | Journal of applied probability 1987-12, Vol.24 (4), p.787-797 |
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| container_end_page | 797 |
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| container_issue | 4 |
| container_start_page | 787 |
| container_title | Journal of applied probability |
| container_volume | 24 |
| creator | Todorovic, P. Gani, J. |
| description | 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} |
| doi_str_mv | 10.2307/3214205 |
| format | Article |
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1} <∞, and 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.</description><identifier>ISSN: 0021-9002</identifier><identifier>EISSN: 1475-6072</identifier><identifier>DOI: 10.2307/3214205</identifier><identifier>CODEN: JPRBAM</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Applications ; Crop production ; Differential equations ; Erosion ; Exact sciences and technology ; Food crops ; Laplace transformation ; Markov chains ; Martingales ; Mathematics ; Probability and statistics ; Random variables ; Research Papers ; Sciences and techniques of general use ; Soil erosion ; Statistics ; Transition probabilities</subject><ispartof>Journal of applied probability, 1987-12, Vol.24 (4), p.787-797</ispartof><rights>Copyright © Applied Probability Trust 1987</rights><rights>Copyright 1987 Applied Probability Trust</rights><rights>1988 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c247t-46233b40d1ebdcc365eb8a6d45ddd1026f11d6081afc9e72cd63ab66ecb460363</citedby><cites>FETCH-LOGICAL-c247t-46233b40d1ebdcc365eb8a6d45ddd1026f11d6081afc9e72cd63ab66ecb460363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3214205$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/3214205$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27923,27924,58016,58020,58249,58253</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7698673$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Todorovic, P.</creatorcontrib><creatorcontrib>Gani, J.</creatorcontrib><title>Modeling the effect of erosion on crop production</title><title>Journal of applied probability</title><addtitle>Journal of Applied Probability</addtitle><description>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} <∞, and 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.</description><subject>Applications</subject><subject>Crop production</subject><subject>Differential equations</subject><subject>Erosion</subject><subject>Exact sciences and technology</subject><subject>Food crops</subject><subject>Laplace transformation</subject><subject>Markov chains</subject><subject>Martingales</subject><subject>Mathematics</subject><subject>Probability and statistics</subject><subject>Random variables</subject><subject>Research Papers</subject><subject>Sciences and techniques of general use</subject><subject>Soil erosion</subject><subject>Statistics</subject><subject>Transition probabilities</subject><issn>0021-9002</issn><issn>1475-6072</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1987</creationdate><recordtype>article</recordtype><recordid>eNp9j01LxDAQhoMoWFfxL-QgiIfq5KOT7VEWV4UVL3ouaT7Wlm5Tku7Bf29lix4EYZiB4eF9eQi5ZHDLBag7wZnkUByRjElV5AiKH5MMgLO8nPYpOUupBWCyKFVG2Euwrmv6LR0_HHXeOzPS4KmLITWhp9OYGAY6xGD3Zpxe5-TE6y65i_kuyPv64W31lG9eH59X95vccKnGXCIXopZgmautMQILVy81WllYaxlw9IxZhCXT3pROcWNR6BrRmVoiCBQLcn3InfpTis5XQ2x2On5WDKpv02o2ncirAznoZHTno-5Nk35wheUSlfjF2jSG-E_azdyrd3Vs7NZVbdjHfnL9w34BwZFpgw</recordid><startdate>19871201</startdate><enddate>19871201</enddate><creator>Todorovic, P.</creator><creator>Gani, J.</creator><general>Cambridge University Press</general><general>Applied Probability Trust</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19871201</creationdate><title>Modeling the effect of erosion on crop production</title><author>Todorovic, P. ; Gani, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c247t-46233b40d1ebdcc365eb8a6d45ddd1026f11d6081afc9e72cd63ab66ecb460363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1987</creationdate><topic>Applications</topic><topic>Crop production</topic><topic>Differential equations</topic><topic>Erosion</topic><topic>Exact sciences and technology</topic><topic>Food crops</topic><topic>Laplace transformation</topic><topic>Markov chains</topic><topic>Martingales</topic><topic>Mathematics</topic><topic>Probability and statistics</topic><topic>Random variables</topic><topic>Research Papers</topic><topic>Sciences and techniques of general use</topic><topic>Soil erosion</topic><topic>Statistics</topic><topic>Transition probabilities</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Todorovic, P.</creatorcontrib><creatorcontrib>Gani, J.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Journal of applied probability</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Todorovic, P.</au><au>Gani, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Modeling the effect of erosion on crop production</atitle><jtitle>Journal of applied probability</jtitle><addtitle>Journal of Applied Probability</addtitle><date>1987-12-01</date><risdate>1987</risdate><volume>24</volume><issue>4</issue><spage>787</spage><epage>797</epage><pages>787-797</pages><issn>0021-9002</issn><eissn>1475-6072</eissn><coden>JPRBAM</coden><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} <∞, and 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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.2307/3214205</doi><tpages>11</tpages></addata></record> |
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| ispartof | Journal of applied probability, 1987-12, Vol.24 (4), p.787-797 |
| issn | 0021-9002 1475-6072 |
| language | eng |
| recordid | cdi_crossref_primary_10_2307_3214205 |
| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing |
| subjects | Applications Crop production Differential equations Erosion Exact sciences and technology Food crops Laplace transformation Markov chains Martingales Mathematics Probability and statistics Random variables Research Papers Sciences and techniques of general use Soil erosion Statistics Transition probabilities |
| title | Modeling the effect of erosion on crop production |
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