Harvesting in a random environment: Itô or Stratonovich calculus?

Journal of Theoretical Biology

Volumn 244, Issue 3, 2007, Pages 424-432

  Braumann, Carlos A ^a  

^a UNIVERSITY OF ÉVORA   (Portugal)

Author keywords

Harvesting models; It calculus; Stationary density; Stochastic differential equations; Stratonovich calculus

Indexed keywords

EQUATION; POPULATION SIZE;

ARTICLE; CALCULATION; GROWTH RATE; HARVEST; ITO CALCULUS; MATHEMATICAL ANALYSIS; MATHEMATICS; PARAMETER; POPULATION SIZE; PRIORITY JOURNAL; PROBABILITY; QUALITATIVE ANALYSIS; QUANTITATIVE ANALYSIS; RANDOMIZATION; SEMANTICS; SPECIES EXTINCTION; STANDARD; STOCHASTIC MODEL; STRATONOVICH CALCULUS;

ANIMALS; FISHERIES; FISHES; FOOD INDUSTRY; MATHEMATICS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; POPULATION DYNAMICS; STOCHASTIC PROCESSES;

EID: 33845896007     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2006.08.029     Document Type: Article

References (37)

1. Alvarez L.H.R. On the option interpretation of rational harvesting planning. J. Math. Biol. 40 (2000) 383-405
2. Alvarez L.H.R., and Shepp L.A. Optimal harvesting in stochastically fluctuating populations. J. Math. Biol. 37 (1997) 155-177
3. Arnold L. Stochastic Differential Equations: Theory and Applications (1974), Wiley, New York
4. Beddington J.R., and May R.M. Harvesting natural populations in a randomly fluctuating environment. Science 197 (1977) 463-465
5. Braumann C.A. Population extinction probabilities and methods of estimation for population stochastic differential equation models. In: Bucy R.S., and Moura J.M.F. (Eds). Nonlinear Stochastic Problems (1983), D. Reidel, Dordrecht 553-559
6. Braumann C.A. Population growth in random environments. Bull. Math. Biol. 45 (1983) 635-641
7. Braumann C.A. Stochastic differential equation models of fisheries in an uncertain world: extinction probabilities, optimal fishing effort, and parameter estimation. In: Capasso V., Grosso E., and Paveri-Fontana L.S. (Eds). Mathematics in Biology and Medicine (1985), Springer, Berlin 201-206
8. Braumann C.A. General models of fishing with random growth parameters. In: Demongeot J., and Capasso V. (Eds). Mathematics Applied to Biology and Medicine (1993), Wuerz, Winnipeg 155-161
9. Braumann C.A. Threshold crossing probabilities for population growth models in random environments. J. Biol. Syst. 3 (1995) 505-517
10. Braumann C.A. Estimação de parâmetros em modelos de crescimento e pesca em ambientes aleatórios. In: Branco J., Gomes P., and Prata J. (Eds). Bom Senso e Sensibilidade, Traves Mestras da Estatística (1996), SPE and Edições Salamandra, Lisboa 103-117
11. Braumann, C.A., 1997. Parameter estimation in population growth and fishing models in random environments. Bulletin of the Intlernational Statistical Institute LVII-CP1, pp. 21-22.
12. Braumann C.A. Applications of stochastic differential equations to population growth. In: Bainov D. (Ed). Proceedings of the Ninth International Colloquium on Differential Equations (1999), VSP, Utrecht 47-52
13. Braumann C.A. Variable effort fishing models in random environments. Math. Biosci. 156 (1999) 1-19 10.1016/S0025-5564(98)10058-5
14. Braumann C.A. Constant effort and constant quota fishing policies with cut-offs in a random environment. Nat. Res. Model. 14 (2001) 199-232
15. Braumann C.A. Variable effort harvesting models in random environments: generalization to density-dependent noise intensities. Math. Biosci. 177&178 (2002) 229-245 10.1016/S0025-5564(01)00110-9
16. Braumann, C.A., 2003. Modeling population growth in random environments: Ito or Stratonovich calculus?. Bulletin of the International Statistical Inst. LX CP1, pp.119-120.
17. Braumann, C.A., 2005. Ito versus Stratonovich calculus in random population growth. Math. Biosc. (accepted for publication). doi:10.1016/j.mbs.2004.09.002
18. Capocelli R.M., and Ricciardi L.M. A diffusion model for population growth in a random environment. Theor. Popul. Biol. 5 (1974) 28-41
19. Dennis B., and Patil G.P. The gamma distribution and weighted multimodal gamma distributions as models of population abundance. Math. Biosci. 68 (1984) 187-212 10.1016/0025-5564(84)90031-2
20. Feldman M.W., and Roughgarden J. A population's stationary distribution and chance of extinction in a stochastic environment with remarks on the theory of species packing. Theor. Popul. Biol. 7 (1975) 197-207
21. Ghiman I.I., and Skorohod A.V. Stochastic Differential Equations (1972), Springer, Berlin
22. Gleit A. Optimal harvesting in a continuous time with stochastic growth. Math. Biosci. 41 (1978) 112-123 10.1016/0025-5564(78)90069-X
23. Guess H.A., and Gillespie J.H. Diffusion approximations to linear stochastic difference equations with stationary coefficients. J. Appl. Probab. 14 (1977) 58-74
24. Karatzas I., and Shreve S.E. Brownian Motion and Stochastic Calculus. second ed (1991), Springer, New York
25. Karlin S., and Taylor H.M. A Second Course in Stochastic Processes (1981), Academic Press, New York
26. Levins R. The effect of random variations of different types on population growth. Proc. Natl Acad. Sci. USA 62 (1969) 1062-1065
27. Lungu E., and Øksendal B. Optimal harvesting from a population in a stochastic crowded environment. Math. Biosci. 145 (1997) 47-75 10.1016/S0025-5564(97)00029-1
28. May R.M. Stability in randomly fluctuating versus deterministic environments. Am. Nat. 107 (1973) 621-650
29. May R.M. Stability and Complexity in Model Ecosystems. second ed (1974), Princeton University Press, New Jersey
30. May R.M., and MacArthur R.H. Niche overlap as a function of environmental variability. Proc Natl Acad. Sci. USA 69 (1972) 1109-1113
31. May R.M., Beddington J.R., Horwood J.H., and Shepherd J.G. Exploiting natural populations in an uncertain world. Math. Biosci. 42 (1978) 219-252 10.1016/0025-5564(78)90097-4
32. Nobile, A.G., Ricciardi, L.M., 1979. Growth and extinction in random environments, in: Proceedings of the INFO II, Patras.
33. Øksendal B. Stochastic Differential Equations. An Introduction with Applications. fifth ed (1998), Springer, Berlin
34. Ricciardi L.M. On a conjecture concerning population growth in random environment. Biol. Cybernet. 32 (1979) 95-99
35. Tuckwell H.C. A study of some diffusion models of population growth. Theor. Popul. Biol. 3 (1974) 345-357
36. Turelli M. Random environments and stochastic calculus. Theor. Popul. Biol. 12 (1977) 140-178
37. Turelli M. A reexamination of stability in randomly varying environments with comments on the stochastic theory of limiting similarity. Theor. Popul. Biol. 13 (1978) 244-267