請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/59876完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Hsin-Lun Li | en |
| dc.contributor.author | 李欣倫 | zh_TW |
| dc.date.accessioned | 2021-06-16T09:42:39Z | - |
| dc.date.available | 2019-02-16 | |
| dc.date.copyright | 2017-02-16 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-02-04 | |
| dc.identifier.citation | [1] Xuerong Mao (2007), Stochastic di erential equations and applications
Second edition [2] Arnold, L. (1974), Stochastic Di erential Equations: Theory and Applications, John Wiley and Sons. [3] Arnold, L. and Crauel, H. (1991), Random dynamical system, Lecture Notes in Mathematics 1486, pp1{22. [4] Arnold, L. and Kliemann, W. (1987), On unique ergodicity for degenerate di usions, Stochastics 21, pp41{61. [5] Arnold, L., Oeljeklaus, E. and Pardoux, E. (1984), Almost sure and moment stability for linear It^o equations, Lecture Note in Math. 1186, pp129{159. [6] Bahar, A. and Mao, X. (2004a), Stochastic delay population dynamics, Journal of International Applied Math. 11(4),pp377{400. [7] Bahar, A. and Mao, X. (2004b), Stochastic delay Lotka-Volterra model, J. Math. Anal. Appl. 292, pp364{380. [8] Baxendale, P. (1994), A stochastic Hopf bifurcation, Probab. Theory Relat. Fields 99, pp581{616. [9] Baxendale, P. and Henning, E.M. (1993), Stabilization of a linear system, Random Comput. Dyn. 1(4), pp395{421. [10] Beckenbach, E.F. and Bellman, R. (1961), Inequalities, Springer. [11] Bell, D.R. and Mohammed, S.E.A. (1989), On the solution of stochastic di erential equations via small delays, Stochastics and Stochastics Reports 29, pp293{299. [12] Bellman, R. and Cooke, K.L. (1963), Di erential{Di erence Equations, Academic Press. [13] Bensoussan, A. (1982), Lectures on stochastic control, Lecture Notes in Math. 972, Springer. [14] Bihari, I. (1957), A generalization of a lemma of Bellman and its application to uniqueness problem of di erential equations, Acta Math. Acad. Sci. Hungar. 7, pp71{94. [15] Bismut, J.M. (1973), Theorie probabiliste du contr^ole des di usions, Mem. Amer. Math. Soc. No. 176. [16] Black, F. and Scholes, M. (1973), The prices of options and corporate liabilities, J. Political Economy 81, 637{654. [17] Brayton, R.(1976), Nonlinear oscillations in a distributed network, Quart. Appl. Math. 24, pp289{301. [18] Bucy, H.J. (1965), Stability and positive supermartingales, J. Differential Equation 1, pp151{155. [19] Carmona, R. and Nulart, D. (1990), Nonlinear Stochastic Integrators, Equations and Flows, Gordon and Breach. [20] Chan, K.C., Karolyi, G.A., Longsta , F.A. and Sanders, A.B. (1992), An empirical comparison of alternative models of the short term interest rate, Journal of Finance 47, pp1209{1227. [21] Chow, P. (1982), Stability of nonlinear stochastic evolution equations, J. Math. Anal. Appl. 89, pp400{419. [22] Coddington, R.F. and Levinson, N. (1955), Theory of Ordinary Differential Equations, McGraw{Hill. [23] Curtain, R.F. and Pritchard, A.J. (1978), In nite Dimensional Linear System Theory, Lecture Notes in Control and Information Sciences 8, Springer. [24] Da Prato, G. and Zabczyk, J. (1992), Stochastic Equations in In - nite Dimensions, Cambridge University Press. [25] Davis, M. (1994), Linear Stochastic Systems, Chapman and Hall. [26] Dellacherie, C. and Meyer, P.A. (1980), Probabilites et Potentiels, 2e edition, Chapitres V{VIII, Hermann. [27] Denker, J.S.(1986), Neural Networks for Computing, Proceedings of the Conference on Neural Networks for Computing (Snowbird, UT, 1986), AIP, New York, 1986. [28] Doleans-Dade, C. and Meyer, P.A. (1977), Equations Di erentilles Stochastiques, Sem. Probab. XI, Lect. Notes in Math. 581. [29] Doob, J.L. (1953), Stochastic Processes, John Wiley. [30] Driver, R.D. (1963), A functional di erential system of neutral type arising in a two-body problem of classical electrodynamics, in Nonlinear Di erential Equations and Nonlinear Mechanics,' Academic Press, pp474{484. [31] Dunkel, G. (1968), Single-species model for population growth depending on past history, Lecture Notes in Math. 60, pp92{99. [32] Dynkin,E.B. (1963), The optimum choice of the instant for stopping a Markov process, Soviet Mathematics 4, 627{629. [33] Dynkin, E.B. (1965), Markov Processes, Vol.1 and 2, Springer. [34] Elliott, R.J. (1982), Stochastic Calculus and Applications, Springer. [35] Elworthy, K.D. (1982), Stochastic Di erential Equations on Manifolds, London Math. Society, Lect. Notes Series 70, C. U. P. [36] Ergen, W.K. (1954), Kinetics of the circulating fuel nuclear reaction, J. Appl. Phys. 25, pp702{711. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/59876 | - |
| dc.description.abstract | 於此篇文章我們將透過週期性成長之隨機延遲物種系統探討物種的延
續與滅絕並探討在什麼情形下物種得以延續，什麼情形下物種會滅絕 以及物種在不同情形下的表現。 | zh_TW |
| dc.description.abstract | In this say, we probe the persistence and extinction of species via Stochastic Delay Lotka-Volterra model with periodic functions to depict seasonal growth of species. We will discuss under what circumstances the solution
to the model is positive almost surely and under what circumstances it exterminates. We also probe properties of the solution to the model under different circumstances. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T09:42:39Z (GMT). No. of bitstreams: 1 ntu-106-R03221008-1.pdf: 791344 bytes, checksum: 9f1a6e3e1c6c2dab99425d4bf28031b3 (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 中文摘要I
英文摘要II 1 Introduction p1 1.1 Background . . . . . . . . . .. . . . . . . . . . . 1 1.2 Prerequisites . . . . . . . . . .. . . . . . . . . . 2 1.2.1 Theorem 1.1 . . . . . . . . . . . . . . . . . . . 3 1.2.2 Theorem 1.2 . . . . . . . . . . . . . . . . . . . 3 1.2.3 Theorem 1.3 . . . . . . . .. . . . . . . . . . . . 3 1.2.4 Lemma . . . . . . . . . . . . . . . . . . . . . . 3 2 Main Theorems p4 2.1 Outline . . . . . . . . . .. . . . .. . . . . . . . 4 2.2 Statements and Proofs . . . . . . . . . . . . . . . 4 2.2.1 Theorem 1 . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Theorem 2 . . . . . . . . . . . . . . . . . . . . 6 2.2.3 Theorem 3 . . . . . . . . . . . . . . . . . . . . 7 2.2.4 Theorem 4 . . . . . . . . . . . . . . . . . . . . 9 2.2.5 Theorem 5 . . . . . . . . . . . . . . . . . . . . 12 2.2.6 Theorem 6 . . . . . . . . . . . . . . . . . . . . 15 2.2.7 Theorem 7 . . . . . . . . . . . . . . . . . . . . 17 2.2.8 Theorem 8 . . . . . . . . . . . . . . . . . . . . 20 2.2.9 Theorem 9 . . . . . . . . . . . . . . . . . . . . 23 2.2.10 Theorem 10 . . . . . . . . . . . . . . . . . . . 25 2.2.11 Theorem 11 . . . . . . . . . . . . . . . . . . . 28 3 Conclusion p30 References p31 | |
| dc.language.iso | en | |
| dc.subject | 強大數法則 | zh_TW |
| dc.subject | 布朗運動 | zh_TW |
| dc.subject | Gronwall不等式 | zh_TW |
| dc.subject | Ito不等式 | zh_TW |
| dc.subject | 隨機延遲物種系統 | zh_TW |
| dc.subject | Ito formula | en |
| dc.subject | Strong law of large numbers | en |
| dc.subject | Stochastic Delay Population System | en |
| dc.subject | Brownian motion | en |
| dc.subject | Gronwall inequality | en |
| dc.title | 週期性成長之隨機延遲物種系統 | zh_TW |
| dc.title | STOCHASTIC DELAY POPULATION SYSTEMS
WITH PERIODIC GROWTH RATE | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王振男(Jenn-Nan Wang),夏俊雄(Chun-Hsiung Hsia) | |
| dc.subject.keyword | 布朗運動,Gronwall不等式,Ito不等式,隨機延遲物種系統,強大數法則, | zh_TW |
| dc.subject.keyword | Brownian motion,Gronwall inequality,Ito formula,Stochastic Delay Population System,Strong law of large numbers, | en |
| dc.relation.page | 33 | |
| dc.identifier.doi | 10.6342/NTU201700338 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2017-02-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-106-1.pdf 未授權公開取用 | 772.8 kB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。