Equivalence and bifurcations of finite order stochastic processes
Diks, Cees and Wagener, Florian O. O. (2005) Equivalence and bifurcations of finite order stochastic processes. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. (Working papers (Warwick Business School. Financial Econometrics Research Centre)).
WRAP_Diks_fwp05-05.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
This article presents an equivalence notion of finite order stochastic processes. Local dependence measures are defined in terms of ratios of joint and marginal probability densities. The dependence measures are classified topologically using level sets. The corresponding bifurcation theory is illustrated with some simple examples.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
|Divisions:||Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School
|Library of Congress Subject Headings (LCSH):||Equivalence classes (Set theory), Bifurcation theory, Stochastic processes, Dependence (Statistics)|
|Series Name:||Working papers (Warwick Business School. Financial Econometrics Research Centre)|
|Publisher:||Warwick Business School, Financial Econometrics Research Centre|
|Place of Publication:||Coventry|
|Date:||25 April 2005|
|Number of Pages:||30|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Netherlands Organisation for Scientific Research] (NWO)|
|References:|| I.S. Abramson, On bandwidth variation in kernel estimates - a square root law, Annals of Statistics 10 (1982), 1217–1223.  L. Arnold, Random dynamical systems, Springer, Heidelberg, 1998.  L. Cobb, Stochastic catastrophe models and multimodal distributions, Behavioral Science 23 (1978), 360–374.  M.A.H. Dempster, I.V. Evstigneev, and K.R. Schenk-Hoppé, Exponential growth of fixed-mix strategies in stationary asset markets, Finance and Stochastics 7 (2003), 263–276.  B.A. Dubrovin, A.T. Fomenko, and S.P. Novikov, Modern Geometry — Methods and Applications. Part II: The Geometry and Topology of Manifolds, Graduate Texts in Mathematics, vol. 104, Springer, New York, 1985.  M.W. Hirsch, Differential Topology, Graduate Texts in Mathematics, vol. 33, Springer, New York, 1976.  P.W. Holland and Y. J.Wang, Dependence function for bivariate densities, Communications in Statistics A 16 (1987), 863–876.  M. C. Jones, The local dependence function, Biometrika 83 (1996), 899–904.  A. Lasota and M.C. Mackey, Chaos, fractals, and noise: Stochastic aspects of dynamics, Springer, Heidelberg, 1994, 2nd edition.  S. Nadarajah, K. Mitov, and S. Kotz, Local dependence functions for extreme value distributions, Journal of Applied Statistics 30 (2003), 1081–1100.  John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces. 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer, 1980.  A. Ploeger, H. L. J. van der Maas, and P. Hartelman, Catastrophe Analysis of Switches in the Perception of Apparent Motion, Psychonomic Bulletin & Review 9 (2002), 26–42.  G.R. Terrell and D.W. Scott, Variable kernel density estimation, Annals of Statistics 20 (1992), 1236–1265.  René Thom, Structural stability and morphogenesis. An outline of a general theory of models, W. A. Benjamin, Reading, Massachusetts, 1975.  E.C. Zeeman, Stability of dynamical systems, Nonlinearity 1 (1988), 115–155.|
Actions (login required)