Construction of equivalent stochastic differential equation models

Stochastic Analysis and Applications

Volumn 26, Issue 2, 2008, Pages 274-297

  Allen, Edward J ^a   Allen, Linda J S ^a   Arciniega, Armando ^b   Greenwood, Priscilla E ^c  

^a TEXAS TECH UNIVERSITY   (United States)

^b UNIVERSITY OF TEXAS AT SAN ANTONIO   (United States)

^c ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Chemical reactions; Cotton fiber breakage; Epidemiology; Mathematical model; Stochastic differential equation

Indexed keywords

EID: 40549105092     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362990701857129     Document Type: Article

References (30)

1. Allen, E.J. 2007. Modeling with Itô Stochastic Differential Equations. Springer, Dordrecht.
2. Allen, E.J. 1999. Stochastic differential equations and persistence time of two interacting populations. Dynamics of Continuous, Discrete, and Impulsive Systems 5:271-281.
3. Allen, E.J., and Victory, H.D. 2003. Modelling and simulation of a schistosomiasis infection with biological control. Acta Tropica 87:251-267.
4. Allen, E.J., Allen, L.J.S., and Schurz, H. 2005. A comparison of persistence-time estimation for discrete and continuous population models that include demographic and environmental variability. Mathematical Biosciences 196:14-38.
5. Allen, L.J.S. 2003. An Introduction to Stochastic Processes with Applications to Biology, Pearson Education Inc., Upper Saddle River, NJ.
6. Allen, L.J.S., and Allen, E.J. 2003. A comparison of three different stochastic population models with regard to persistence time. Theoretical Population Biology 68:439-449.
7. Allen, L.J.S., McCormack, R.K., and Jonsson, C.B. 2006. Mathematical models for hantavirus infection in rodents. Bulletin of Mathematical Biology 68(3):511-524.
8. Hayes, J.G., and Allen, E.J. 2005. Stochastic point-kinetics equations in nuclear reactor dynamics. Annals of Nuclear Energy 32:572-587.
9. Kirupaharan, N., and Allen, L.J.S. 2004. Coexistence of multiple pathogen strains in stochastic epidemic models with density-dependent mortality. Bulletin of Mathematical Biology 66:841-864.
10. Koskodan, R. 2006. Extrapolation of an Implicit Method for Numerical Solution of Stochastic Differential Equations and Development of a Stock-Price Model with Application to Multi-Asset Option Pricing. Ph.D. Dissertation in Mathematics, Texas Tech University, Lubbock, Texas.
11. Sharp, W.D., and Allen, E.J. 2000. Stochastic neutron transport equations for rod and plane geometries. Annals of Nuclear Energy 27:99-116.
12. Simsek, H. 2007. Stochastic Models for Cotton Fiber Breakage. MS Thesis. Texas Tech University, Lubbock, Texas.
13. Gillespie, D.T. 1976. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22:403-434.
14. Gillespie, D.T. 1977. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81:2340-2361.
15. Gillespie, D.T. 2001. Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics 115:1716-1733.
16. Greenwood, P., Gordillo, L.F., and Kuske, R. 2006. Autonomous stochastic resonance. In M. Huskova and M. Janzura eds., Prague Stochastics, pp. 102-111. Prague, MatFyz Press.
17. Kuske, R., Gordillo, L.F., and Greenwood, P. 2007. Sustained oscillations via coherence resonance in SIR. Journal of Theoretical Biology 245:459-469.
18. Gard, T.C. 1987. Introduction to Stochastic Differential Equations. Marcel Decker, New York.
19. Øksendal, B. 1980. Stochastic Differential Equations. 2nd ed. Springer-Verlag, New York.
20. Kloeden P.E., and Platen, E. 1992. Numerical Solution of Stochastic Differential Equations. Springer-Verlag, New York.
21. Kloeden, P.E., Platen, E., and Schurz, H. 1994. Numerical Solution of SDE Through Computer Experiments. Springer, Berlin.
22. Ortega, J.M. 1987. Matrix Theory: A Second Course. Plenum Press, New York.
23. Watkins, D.S. 1991. Fundamentals of Matrix Computations. John Wiley & Sons, New York.
24. Allen, E.J., Baglama, J., and Boyd, S.K. 2000. Numerical approximation of the product of the square root of a matrix with a vector. Linear Algebra and its Applications 310:167-181.
25. Higham, N.J. 1986. Newton's method for the matrix square root. Mathematics of Computation 46:537-549.
26. Lakić, S., and Petković, M.S. 1998. On the matrix square root. Z. Angew. Math. Mech. (ZAMM) 78:173-182.
27. Krifa, M. 2006. Fiber length distribution in cotton processing: dominant features and interaction effects. Textile Research Journal 76:426-435.
28. Meyer, R., Almin, K.E., and Steenberg, B. 1966. Length reduction of fibres subject to breakage. British Journal of Applied Physics 17:409-416.
29. Arino, J., McCluskey, C.C., and van den Driessche, P. 2003. Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM Journal on Applied Mathematics 64:260-76.
30. Allen, L.J.S., and van den Driessche, P. 2006. Stochastic epidemic models with a backward bifurcation. Mathematical Biosciences and Engineering 3(3):445-458.