Convergence of numerical solution of stochastic differential equation for the self-thinning process
For theoretical and practical analysis of the self-thinning process we use stochastic differential equation, which take the form: dN (t) = N (t) (α - β ln N (t))dt + μN (t)dW (t), N(t0) = N0, t0 ≤ t ≤ T, where N – tree per hectare (stem/ha), t – stand age, W(t) – scalar standard Brownian motion...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2002-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/32840 |
| _version_ | 1797198402518253568 |
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| author | Petras Rupšys |
| author_facet | Petras Rupšys |
| author_sort | Petras Rupšys |
| collection | DOAJ |
| description |
For theoretical and practical analysis of the self-thinning process we use stochastic differential equation, which take the form:
dN (t) = N (t) (α - β ln N (t))dt + μN (t)dW (t), N(t0) = N0, t0 ≤ t ≤ T,
where N – tree per hectare (stem/ha), t – stand age, W(t) – scalar standard Brownian motion, N0 – not random, α, β and μ are parameters – real constants. In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. The programs for numerical simulation are written on MAPLE. The convergence of this model is explored too.
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| first_indexed | 2024-03-07T14:22:48Z |
| format | Article |
| id | doaj.art-ea664f2f78084066bf80c503abd7eca7 |
| institution | Directory Open Access Journal |
| issn | 0132-2818 2335-898X |
| language | English |
| last_indexed | 2024-04-24T06:59:17Z |
| publishDate | 2002-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj.art-ea664f2f78084066bf80c503abd7eca72024-04-22T09:04:18ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2002-12-0142spec.10.15388/LMR.2002.32840Convergence of numerical solution of stochastic differential equation for the self-thinning processPetras Rupšys0Lithuanian Academy of Agriculture For theoretical and practical analysis of the self-thinning process we use stochastic differential equation, which take the form: dN (t) = N (t) (α - β ln N (t))dt + μN (t)dW (t), N(t0) = N0, t0 ≤ t ≤ T, where N – tree per hectare (stem/ha), t – stand age, W(t) – scalar standard Brownian motion, N0 – not random, α, β and μ are parameters – real constants. In this paper from a practical viewpoint we apply a simple numerical method for solution of the stochastic differential equations by the Milstein's higher order method. The programs for numerical simulation are written on MAPLE. The convergence of this model is explored too. https://www.zurnalai.vu.lt/LMR/article/view/32840 |
| spellingShingle | Petras Rupšys Convergence of numerical solution of stochastic differential equation for the self-thinning process Lietuvos Matematikos Rinkinys |
| title | Convergence of numerical solution of stochastic differential equation for the self-thinning process |
| title_full | Convergence of numerical solution of stochastic differential equation for the self-thinning process |
| title_fullStr | Convergence of numerical solution of stochastic differential equation for the self-thinning process |
| title_full_unstemmed | Convergence of numerical solution of stochastic differential equation for the self-thinning process |
| title_short | Convergence of numerical solution of stochastic differential equation for the self-thinning process |
| title_sort | convergence of numerical solution of stochastic differential equation for the self thinning process |
| url | https://www.zurnalai.vu.lt/LMR/article/view/32840 |
| work_keys_str_mv | AT petrasrupsys convergenceofnumericalsolutionofstochasticdifferentialequationfortheselfthinningprocess |