Accelerated Genetic Algorithm Solutions Of Some Parametric Families Of Stochastic Differential Equations
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AUTHOR(S)
Eman Ali Hussain, Yaseen Merzah Alrajhi
KEYWORDS
Index Terms: accelerated genetic algorithm, stochastic differential equations, Ito formula
ABSTRACT
Absract: In this project, A new method for solving Stochastic Differential Equations (SDEs) deriving by Wiener process numerically will be construct and implement using Accelerated Genetic Algorithm (AGA). An SDE is a differential equation in which one or more of the terms and hence the solutions itself is a stochastic process. Solving stochastic differential equations requires going away from the recognizable deterministic setting of ordinary and partial differential equations into a world where the evolution of a quantity has an inherent random component and where the expected behavior of this quantity can be described in terms of probability distributions. We applied our method on the Ito formula which is equivalent to the SDE, to find approximation solution of the SDEs. Numerical experiments illustrate the behavior of the proposed method.
REFERENCES
[1] S. M. Iacus , "Simulation and Inference for Stochastic Differential Equations , " Springer Science +Business Media, LLC , (2008).
[2] T.T. Soong, "Random differential equations in science and engineering," Academic Press, New York. L c Number: A274.23.S58., (1973).
[3] D. Henderson, and P. Plaschko , "Stochastic differential equations in science and engineering," World Scientific,(2006).
[4] K. Ito, "Stochastic integral," Tokyo, Proc. Jap. Acad , 20, pp. 519529, (1944).
[5] E. Allen, "Modeling with Ito stochastic differential equations," SpringerVerlag.(2007).
[6] F.C. Klebaner , "Introduction to Stochastic Calculus with Applications," Imperial College Press, (2005).
[7] Y . Saito, T. Mitsui, "Simulation of Stochastic Differential Equations," The Annals of the Institute of Statistical Mathematics, 3, 419432. (1993).
[8] P. E. Kloeden ,"A survey of numerical methods for stochastic differential Equations," Stochastic Hydrology and Hydraulics, 3, 155178, (1989).
[9] P.E. Kloeden, E. Platen, "Relations between multiple Ito and stratonovich Integrals," Stochastic Analysis and Applications, 9(3), 311321, (1991a).
[10] P.E. Kloeden, , E. Platen, "Stratonovich and Ito stochastic Taylor expansions," Mathematics Nachrichten , 151, 3350, (1991b).
[11] P.E. Kloeden, E.Platen, "Numerical Solution of Stochastic Differential Equations," Springer Verlag, New York, (1995).
[12] P.E. Kloeden, E. Platen, and H. Schurz, "Numerical solution of SDE through computer experiments," SpringerVerlag, New York, (1994).
[13] B. Oksendal, "Stochastic Differential Equations: An Introduction with Applications," 5th edition. Springer Verlag, Berlin, (2000).
[14] G. Tsoulos .I.E, "Solving differential equations with genetic programming ," P.O. Box 1186 , Ioannina 45110, (2003).
[15] E.A. Hussain and Y.M. Alrajhi , "Solution of partial differential equations using accelerated genetic algorithm," Int. J. of Mathematics and Statistics Studies,Vol.2, No.1, pp.5569, March (2014).
[16] P. Naur , "evised report on the algorithmic language ALGOL,"(1963).
[17] M. O'Neill and C. Ryan, "Under the hood of grammatical evolution,"(1999).
[18] M. O'Neill and C. Ryan, "Grammatical Evolution: Evolutionary Automatic Programming in a Arbitrary Language," Kluwer Academic Publishers, (2003).
[19] M. O'Neill and C. Ryan, "Grammatical Evolution, " IEEE Trans. Evolutionary Computation, Vol. 5, pp. 349358, (2001).
[20] A. Sydow, "GMDFIRST Genetic Algorithms and Genetic Programming Modern Concepts and Practical Applications , " Berlin, Germany, (2009)
[21] D.E. Goldberg, "Genetic algorithms in search, Optimization and Machine Learning, "Addison Wesley, (1989).
[22] E.A. Hussain and Y. M. Alrajhi , "Accelerated Genetic Algorithm Solution of Linear Black – Scholes Equation" , IJMCAR. (2014).
