Integration of stochastic ordinary differential equations from a symmetry standpoint

Journal of Physics A: Mathematical and General

Volumn 34, Issue 1, 2001, Pages 177-192

  Wafo Soh, C ^a   Mahomed, F M ^a  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039838712     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/1/314     Document Type: Article

References (30)

1. Gaeta G and Quintero N R 1999 Lie-point symmetries and stochastic differential equations J. Phys. A: Math. Gen. 32 8485-595
2. Milatz J M W and Zolingen V J J 1953 Physica 19 181
3. Boyce W E 1961 The bending of columns under axial loads of random eccentricity Renselaer Polytechnic Institute Research Report No 43
4. Lyon R H 1966 J. Acoust. Soc. Am. 32 1161
5. Ludwig D 1974 Stochastic Population Theories (Lecture Notes in Biomath vol 3) (Berlin: Springer)
6. Larnberton D and Lapeyre B 1996 Introduction to Stochastic Calculus Applied to Finance (London: Chapman and Hall)
7. Bogdanoff J L, Goldberg J E and Bernard M C 1961 Response of a simple structure to a random earthquake-type disturbance Bull Seism. Soc. Am. 51 293-310
8. Liepmann H W 1952 On the application of statistical concepts to buffeting problem J. Aerosp. Sci. 19 793-800
9. Kelly F P and Williams R J (ed) 1995 Stochastic networks The IMA Volumes in Mathematics and its Applications vol 71
10. Olver P J 1986 Applications of Lie Groups to Differential Equations (New York: Springer)
11. Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Springer)
12. Stephani H 1989 Differential Equations - Their Solutions Using Symmetries (Cambridge: Cambridge University Press)
13. Ibragimov N H 1999 Elementary Lie Group Analysis and Ordinary Differential Equations (New York: Wiley)
14. Feller W 1957 An Introduction to Probability Theory and Its Applications vol 1 (New York: Wiley)
15. Wiener N 1923 Differential space J. Math. Phys. 2 131-74
16. Ito K 1951 On Stochastic Differential Equations (Mem. Am. Math. Soc. 4) (Providence, RI: American Mathematical Society)
17. Gard T C 1988 Introduction to Stochastic Differential Equations (New York: Dekker)
18. Oksendal B 1998 Stochastic Differential Equations: an Introduction with Applications (Berlin: Springer)
19. Soong T T 1973 Random Differential Equations in Sciences and Engineering (New York: Academic)
20. Srinivasan S K and Vasudevan R 1971 Introduction to Random Differential Equations and Their Applications (New York: Elsevier)
21. Lie S 1891 Differentialgleichungen (Leipzig: Teubner); reprinted 1967 (New York: Chelsea)
22. Bianchi L 1918 Lezioni Sulla Teori dei Gruppi Continui Finiti di Transformazioni (Pisa: Spoerri)
23. Mahomed F M 1989 Symmetry Lie algebras of nth order ordinary differential equations PhD Thesis University of the Witwatersrand, Johannesburg
24. Mahomed F M and Ibragimov N H 1996 Ordinary differential equation CRC Handbook of Lie Group Analysis of Differential Equations (Boca Raton, FL: Chemical Rubber Company) ch 8, pp 191-215
25. Mubarakzyanov G M 1963 Izv. Vyssh. Uchebn. Zaved. Nath. 32(1) 114 (in Russian)
26. Mubarakzyanov G M 1963 Izv. Vyssh. Uchebn. Zaved. Nath. 34(2) 99 (in Russian)
27. Mubarakzyanov G M 1963 Izv. Vyssh. Uchebn. Zaved. Nath. 35(4) 104 (in Russian)
28. Patera J and Winternitz P 1977 Subalgebras of real three- and four-dimensional Lie algebras J. Math. Phys. 18 1449-55
29. Turkowski P 1988 Low-dimensional real Lie algebras J. Math. Phys. 29 2139-44
30. Gaeta G 2000 Lie-point symmetries and stochastic differential equations: II J. Phys. A: Math. Gen. 33 4883-902