Integral Equations To Non-Riemann Cases
Author Affiliations
- 1Department of Statistics, Burdwan University, Burdwan, W.B., INDIA
Res. J. Mathematical & Statistical Sci., Volume 1, Issue (7), Pages 6-12, August,12 (2013)
Abstract
The linear or nonlinear equations are important in many cases of stochastic process viz, renewal equations, age dependent branching process etc. There is a standard theory of linear integral equations. Here the technique is generalised and modified under different set ups. Generalisations are considered in three different cases:i. Integration is Riemann-Stieltjes integration with respect to an integrator of bounded variation, ii. integration w.r.t. step function integrator and iii. integration on any probability space or measure space.
References
- Bhat U.N., Elements of Applied Stochastic Processes, 2nd Ed., Wiley, New York, (1984)
- Volterra V., Lecons sur la theorie mathematiques de la lutte pour la vie, Paris, 214 (1931)
- Hoel P.G., et al, Introduction to Stochastic Processes, Universal Book Stall, New Delhi, (1991)
- Davis H.T., Introduction to Nonlinear Differential and Integral Equations, 1st ed., Dover Publications, Inc., New York,(1962)
- Evans G.C., Some General Types of Functional Equations, Fifth International Congress of Mathmaticians, l(1), 387-396(1912)
- Jordan C., Calculus of Finite Differences, 3rd ed., New York: Chelsea, (1965)
- Ross S.M., Introduction to Probability Models, 6th ed., New York: Academic Press, (1994)
- Ross S.M., Applied Probability Models with Optimization Applications, Dover Publication, (1970)
- Apostal T.M., Mathematical Analysis. Addison-Wesley Publishing Company, Massachusetts, (1973)
- Simmons G.F., Introduction to Topology and Modern Analysis, McGraw-Hill, (1963)
