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Kendall, W. S. (2005)
Publisher: Wolfram Research, Inc.
Languages: English
Types: Article
Subjects: QA
This article explains how the Itovsn3 package can be extended to add\ud various properties and rules for ItoIntegral, which represents a stochastic\ud or Itô integral. This allows us to introduce a further expectation operator\ud and compute suitable expectations involving Itô integrals.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • In[12]:= ItoIntegralRewriteRuleset Module a, b, c, d, conv, l1, l2 , SetAttributes a, b, c, d, conv , Constant ; conv Map # Condition Pattern #, Blank a, b, c, d ; l1 t, ta , B, Bb , t B, t Bb , ta B, ta Bb ; l2 t, tc , B, Bd , t B, t Bd , tc B, tc Bd ; Map # 1 . conv # 2 &, Flatten
    • [5] E. Thönnes, A. Bhalerao, W. S. Kendall, and R. G. Wilson, “A Bayesian Approach to Inferring Vascular Tree Structure from 2D Imagery,” in International Conference on Image Processing, Proceedings ICIP 2002, (W. J. Niessen and M. A. Viergever, eds.), pp. 937-939; University of Warwick Department of Statistics Research Report 391 (Oct 2001) www.warwick.ac.uk/go/wsk/ppt/391.pdf.
    • [6] J. M. Steele and R. A. Stine, “Mathematica and Diffusions,” Economic and Financial Modeling with Mathematica, (H. R. Varian, ed.), New York: Springer-Verlag, 1993 pp. 192-214.
    • [7] M. Fisher, “ItosLemma.m” MathSource (May 20, 2002) library.wolfram.com/database/ MathSource/1170 (or www.markfisher.net/~mefisher/mma/mathematica.html).
    • [8] S. Cyganowski, “Solving Stochastic Differential Equations with Maple” Computer Algebra: Maple Tech, 3(2), 1986 pp. 35-40.
    • [9] J. G. Gaines, “The Algebra of Iterated Stochastic Integrals,” Stochastics and Stochastics Reports, 49(3-4), 1994 pp. 169-179.
    • [10] J. G. Gaines, “A Basis for Iterated Stochastic Integrals,” Mathematics and Computers in Simulation [online], 38(1-3), 1995 pp. 7-11. dx.doi.org/10.1016/0378-4754(93)E0061-9.
    • [11] C. Rose and M. D. Smith, Mathematical Statistics with Mathematica, Springer Texts in Statistics, New York: Springer-Verlag, 2002.
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