An introduction to mathematical analysis for economic theory and econometrics

An Introduction to Mathematical Analysis for Economic Theory and Econometrics

Volumn , Issue , 2009, Pages

  Corbae, Dean ^a   Stinchcombe, Maxwell B ^a   Zeman, Juraj ^a  

^a NONE

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EID: 78649787744     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (42)

1. J. Dugundji's Topology (Boston: Allyn and Bacon, 1966).
2. T. Lindstrøm's "Introduction to nonstandard analysis," Chapter 1 in N. Cutland's Nonstandard Analysis and Its Applications (Cambridge: Cambridge University Press, 1988).
3. A. Mas-Colell, M. D. Whinston, and J. R. Green's Microeconomic Theory (New York: Oxford University Press, 1995).
4. D. M. Topkis, Supermodularity and Complementarity (Princeton, N.J.: Princeton University Press, 1998).
5. A. E. Roth and M. A. Sotomayor's Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis (Cambridge: Cambridge University Press, 1990).
6. H. Adachi ("On a characterization of stable matchings," Economic Letters 68, 43-49).
7. A. N. Kolmogorov and S. V. Fomin's Introductory Real Analysis (translated and edited by R. A. Silverman; New York: Dover, 1975, 1970).
8. K. G. Binmore's The Foundations of Analysis: A Straightforward Introduction (Cambridge: Cambridge University Press, 1980)
9. W. Rudin's Principles of Mathematical Analysis (3rd Ed., New York: McGraw-Hill, 1976)
10. J. E. Marsden and M. J. Hoffman's Elementary Classical Analysis (2nd Ed., New York:W. H. Freeman, 1993)
11. Real Analysis (3rd Ed., New York: Macmillan, 1988)
12. J. E. Marsden and M. J. Hoffman's Elementary Classical Analysis (2nd Ed., New York: W. H. Freeman, 1993)
13. W. Rudin's Principles of Mathematical Analysis (3rd Ed., New York: McGraw-Hill, 1976)
14. J. R. Munkres's Topology (2nd Ed., Upper Saddle River, N.J.: Prentice-Hall, 2000) are three that we are familiar with and like very much.
15. R. T. Rockafellar's Convex Analysis (Princeton, N.J.: Princeton University Press, 1970)
16. T. Ichiishi's Game Theory for Economic Analysis (New York: Academic Press, 1983)
17. Topological Methods in Euclidean Spaces (Cambridge: Cambridge University Press, 1980)
18. G. Naber has a complete proof, at an undergraduate level, of Brouwer's theorem. Linear Operators, Vol. 1 (New York: Interscience, 1958)
19. K. C. Border's Fixed Point Theorems with Applications to Economics and Game Theory (Cambridge: Cambridge University Press, 1985).
20. J. R. Munkres's Topology (2nd Ed., Upper Saddle River, N.J.: Prentice-Hall, 2000)
21. A. N. Kolmogorov and S. V. Fomin's Introductory Real Analysis (translated and edited by R. A. Silverman; New York: Dover, 1975, 1970)
22. E.Ward Cheney's Analysis for Applied Mathematics (New York: Springer-Verlag, 2001).
23. P. Billingsley's Probability and Measure (3rd Ed., New York:Wiley, 1995)
24. C. Dellacherie and P. A. Meyer's advanced monograph, Probabilities and Potential (translated and prepared by J. P. Wilson; Amsterdam: North-Holland, 1982)
25. R. M. Dudley's Real Analysis and Probability (Cambridge: Cambridge University Press, 2002)
26. W. Feller's twovolume classic, An Introduction to Probability Theory and Its Applications (New York: Wiley, 1971)
27. E. Ward Cheney's Analysis for Applied Mathematics (New York: Springer-Verlag, 2001) they occupy a more central place
28. R. M. Dudley's Real Analysis and Probability (Cambridge: Cambridge University Press, 2002)
29. H. L. Royden's Real Analysis (3rd Ed., New York: Macmillan, 1988).
30. D. A. Ross, "An elementary proof of Lyapunov's theorem," American Mathematical Monthly 112(7), 651-53 (2005)
31. L. E. Dubins and E. H. Spanier's "How to cut a cake fairly," American Mathematical Monthly 68(1), 1-17 (1961).
32. Historically, the material in this chapter was first pulled together in textbook form in K. R. Parthasarathy's Probability Measures on Metric Spaces (New York: Academic Press, 1967)
33. P. Billingsley's Convergence of Probability Measures (New York:Wiley, 1968).
34. D. Pollard's Convergence of Stochastic Processes (New York: Springer-Verlag, 1984) is an updated version of this approach that leads one more directly into current research using probability theory in econometrics.
35. A. P. Robertson and W. Robertson's Topological Vector Spaces (2nd Ed., Cambridge: Cambridge University Press, 1973) lays out, with surprising economy and readability, the basics of topology for locally convex vector spaces.
36. Infinite Dimensional Analysis: A Hitchhiker's Guide (3rd Ed., New York: Springer-Verlag, 2006)
37. C. D. Aliprantis and K. C. Border covers a broad range of vector space topics relevant for general equilibrium analysis beyond what we touch.
38. N. L. Carothers's A Short Course on Banach Space Theory (Cambridge: Cambridge University Press, 2005) gives a lovely coverage of the major classical topics in Banach space theory.
39. We learned most of the material in this chapter from T. Lindstrøm's "Introduction to nonstandard analysis," Ch. 1 in N. Cutland's Nonstandard Analysis and Its Applications (Cambridge: Cambridge University Press, 1988)
40. A. E. Hurd and P. A. Loeb's An Introduction to Nonstandard Real Analysis (Orlando, Fla.: Academic Press, 1985).
41. The nonstandard analysis approach to stochastic process theory that grew out of R. Anderson's article, "A nonstandard representation for Brownian motion and It̂ integration," Israel Journal of Mathematics 25, 15-46 (1976)
42. K. D. Stroyan and J. M. Bayod's Foundations of Infinitesimal Stochastic Analysis (Amsterdam: North-Holland, 1986).