Abstract
In this paper we shall refer to some problems involving stochastic calculus, diffusion approximation and Markov processes. Finally a problem of stochastic approximation in genetics systems is discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This problem was firstly discussed in detail by S. Wright and R. A. Fisher. Its Markovian nature was pointed out by G. Malécot in: Sur un problèm de probabilités en chaine que pose la génétique, Comptes Rendus de l’Académie des Sciences, vol. 219, 1944, pp. 379–381. It is also presented at length in [9].
References
Bharucha-Reid, A.T.: Elements of the Theory of Markov Processes and their Applications. Dover, Mineola (1997)
Feller, W.: An Introduction to Probability Theory and its Applications, vol. I. Wiley, New York (1960)
Itô, K.: In: Barndorff-Nielsen, O.E., Sato, K.-i. (eds.) Stochastic Processes. Springer, Berlin (2004)
Itô, K., McKean, H.P., Jr.: Diffusion Processes and Sample Paths. Springer, Berlin (1974)
Øksendal, B.: Stochastic Differential Equations: An Introduction with Applications, 6th edn. Springer, Berlin (2003)
Øksendal, B., Sulem, A.: Applied Stochastic Control of Jump Diffusions. Springer, Berlin (2007)
Orman, G.V. Lectures on Stochastic Approximation Methods and Related Topics. Textbook. “Gerhard Mercator” University, Duisburg, Germany (2001)
Orman, G.V.: Handbook of Limit Theorems and Stochastic Approximation. Transilvania University Press, Brasov (2003)
Orman, G.V.: On Markov processes: a survey of the transition probabilities and Markov property. In: Skiadas, C.H., Dimotikalis, I. (eds.) Chaotic Systems: Theory and Applications, pp. 224–231. World Scientific, Singapore (2010)
Schuss, Z.: Theory and Application of Stochastic Differential Equations. Wiley, New York (1980)
Stroock, D.W.: Markov Processes from K. Itô Perspective. Princeton University Press, Princeton (2003)
Wasan, M.T.: Stochastic Approximation. Cambridge University Press, London (1969)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Orman, G.V., Radomir, I. (2013). On Stochastic Calculus and Diffusion Approximation to Markov Processes. In: Stavrinides, S., Banerjee, S., Caglar, S., Ozer, M. (eds) Chaos and Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33914-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-33914-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33913-4
Online ISBN: 978-3-642-33914-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)