Abstract
There is a fundamental difference between the mathematical formulation of a discrete time stochastic process and a continuous time stochastic process. In discrete time, it is necessary to specify only the mechanism for transition from one state to another, and of course the initial state (distribution) of the system. For Markov chains, this consists of the transition matrix and the initial vector. Everything about the chain can, in principle, be deduced from this matrix and vector.
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
Preview
Unable to display preview. Download preview PDF.
Reference
Çinlar, Erhan (1975), Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, New Jersey.
Cox, D. R. (1962), Renewal Theory, John Wiley and Sons, New York.
Cox, D. R., and Miller, H. D. (1965), The Theory of Stochastic Processes, Methuen, London.
Hoel, Paul G., Port, Sidney C., and Stone, Charles J. (1972), Introduction to Stochastic Processes, Houghton Mifflin, Boston.
Karlin, Samuel, and Taylor, Howard M., (1975), A First Course in Stochastic Processes, Academic Press, New York.
Ross, Sheldon M. (1972), Introduction to Probability Models, Academic Press, New York.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1981 Plenum Press, New York
About this chapter
Cite this chapter
Haight, F.A. (1981). Continuous Time Processes. In: Applied Probability. Mathematical Concepts and Methods in Science and Engineering, vol 23. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6467-6_5
Download citation
DOI: https://doi.org/10.1007/978-1-4615-6467-6_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4615-6469-0
Online ISBN: 978-1-4615-6467-6
eBook Packages: Springer Book Archive