Solution of Stochastic Non-Homogeneous Linear First-Order Difference Equations


In this paper, the closed form solution of the non-homogeneous linear first-order difference equation is given. The studied equation is in the form: xn = x0 + bn, where the initial value x0 and b, are random variables.

Share and Cite:

Kadry, S. and Hami, A. (2014) Solution of Stochastic Non-Homogeneous Linear First-Order Difference Equations. Journal of Mathematical Finance, 4, 245-248. doi: 10.4236/jmf.2014.44021.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Elaydi, S. (2004) An Introduction to Difference Equations. 3rd Edition, Springer-Verlag, New York.
[2] King, F. (2005) Difference Equations [PDF Document]. Retrieved from Lecture Notes Online Web Site:
[3] Chui, C.K. and Chen, G. (1987) Kalman Filtering with Real-Time Applications. 2nd Edition, Springer-Verlag, New York.
[4] Novak, S.Y. (2011) Extreme Value Methods with Applications to Finance. Chapman & Hall/CRC Press, London.
[5] Soong, T.T. (1973) Random Differential Equations in Science and Engineering. Academic Press, New York.
[6] Kadry, S.A. (2007) Solution of Linear Stochastic Differential Equation. USA: WSEAS Transactions on Mathematics, April 2007, 618.
[7] Kadry, S. (2012) Exact Solution of the Stochastic System of Difference Equations. Journal of Mathematical Control Science and Applications (JMCSA), 5, 67-70.
[8] Kadry, S. and Younes, R. (2005) étude Probabiliste d’un Système Mécanique à Paramètres Incertains par une Technique Basée sur la Méthode de transformation. Proceedings of the 20th Canadian Congress of Applied Mechanics (CANCAM’ 05), Montreal, 30 May, 490-491.
[9] Kadry, S. (2012) Probabilistic Solution of Rational Difference Equations System with Random Parameters. ISRN Applied Mathematics, 2012, Article ID: 290186.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.