Solution of Stochastic Non-Homogeneous Linear First-Order Difference Equations ()
Abstract
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.
References
[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: http://www.cl.cam.ac.uk/teaching/2004/Probability/
|
[3]
|
Chui, C.K. and Chen, G. (1987) Kalman Filtering with Real-Time Applications. 2nd Edition, Springer-Verlag, New York. http://dx.doi.org/10.1007/978-3-662-02508-6
|
[4]
|
Novak, S.Y. (2011) Extreme Value Methods with Applications to Finance. Chapman & Hall/CRC Press, London. http://dx.doi.org/10.1201/b11537
|
[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. http://dx.doi.org/10.5402/2012/290186
|