Kendall, Wilfrid S.. (2005) Stochastic integrals and their expectations. The Mathematica Journal, Vol.9 (No.4). ISSN 1097-1610

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Abstract

This article explains how the Itovsn3 package can be extended to add various properties and rules for ItoIntegral, which represents a stochastic or Itô integral. This allows us to introduce a further expectation operator and compute suitable expectations involving Itô integrals.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Stochastic integrals -- Computer programs, Mathematica (Computer file)
Journal or Publication Title:	The Mathematica Journal
Publisher:	Wolfram Research, Inc.
ISSN:	1097-1610
Date:	2005
Volume:	Vol.9
Number:	No.4
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC)
Grant number:	GR/M75785 (EPSRC)
References:	[1] W. S. Kendall, “Itovsn3: Doing Stochastic Calculus with Mathematica,” Economic and Financial Modeling with Mathematica (H. R. Varian, ed.), New York: Springer-Verlag, 1993 pp. 214–239. [2] W. S. Kendall, “Stochastic Calculus in Mathematica: Software and Examples,” University of Warwick Department of Statistics Research Report 333 (Jan 2003) www.warwick.ac.uk/go/wsk/ppt/333.pdf. [3] B. K. Øksendal, Stochastic Differential Equations, 5th ed., Berlin: Springer Universitext, 1998. [4] A. Bhalerao, E. Thönnes, W. S. Kendall, and R. G. Wilson, “Inferring Vascular Structure from 2D and 3D Imagery,” in Medical Image Computing and Computer-Assisted Intervention, Proceedings MICCAI 2001, (W. J. Niessen and M. A. Viergever, eds.), pp. 820–828; Lecture Notes in Computer Science 2208, Springer, 2001 pp. 820–828; University of Warwick Department of Statistics Research Report 392 (Jan 2002) www.warwick.ac.uk/go/wsk/ppt/392.pdf. [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 (May20,2002) 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.
URI:	http://wrap.warwick.ac.uk/id/eprint/37634

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