Shafiqul  Islam


  Research Interests:  

    Ergodic Theory, Dynamical systems,  Stochastic processes, Random dynamical systems  and applications.

 

  Publications:

Articles published in refereed Journals:

1.      Islam, M. S. and Chandler, S. (2015), Approximation by absolutely continuous invariant measures of iterated function systems with position dependent probabilities Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society. 23(4).

2.      Islam, M. S. (2015), Piecewise linear least-squares approximations of invariant measures for random maps: Neural, Parallel, and Scientific Computations. 23

3.      Islam, M. S.(2015). Stochastic perturbations and invariant measures of position dependent random maps via Fourier approximations. International Journal of bifurcation and chaos. 25(9): 15501-12.

4.      Islam, M. S. (2015), Rychlik's Theorem and invariant measures for random mapsof piecewise expanding C1 maps satisfying summableoscillation condition: International Journal of Pure and Applied mathematics. Volume 102 (No 1): 105-116.

5.      Islam, M. S. (2015). Stochastic perturbations and Ulam's method for position dependent random maps satisfying the stronger Lasota-Yorke inequality: Dynamics of Continuous, Discrete and Impulsive Systems (accepted)

6.      Islam, M. S.(2014), A Lasota-Yorke type inequality for position dependent random maps of one dimensional piecewise expanding C1,1 transformations.Dyn. Contin. Discrete Impuls. Syst. Ser. A. 21(1)

7.      Swishchuk, A. and Islam, S. (2013). Random Dynamical Systems in Finance (First Edition), Taylor and Francis (CRC Press)

8.      Islam M. S. (2013), Invariant measures for random maps via interpolations. International Journal of Bifurcation and Chaos. 23(2)

9.      Swishchuk A. and Islam, M. S.(2013). Normal deviations and Poisson approximation of a security market by the geometric Markov renewal processes. Communications in Statistics: Theory and Methods. 42: 1488-1501.

10.      Swishchuk, A. and Islam, M. S. (2011), The Geometric Markov Renewal Processes with Applications to Finance: Stochastic Analysis and Applications. 29(4): 684-705.

11.      Islam M. S.(2011), Maximum Entropy method for position dependent random maps: International Journal of Bifurcation and Chaos. 21(6): 1805 - 1811.

12.      Islam M. S. and Gora P.(2011), Invariant measures of Stochastic perturbations of dynamical systems using Fourier approximations: International Journal of Bifurcations and Chaos. 21(1): 113 -123.

13.      Doosti H., Islam M-S, Chaubey Y. P and Gora P.(2010). Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system. Italian Journal of Pure and Applied Mathematics. 27: 39-62.

14.      Swishchuk A. and Islam, M. S.(2010). Diffusion approximations of the geometric Markov renewal processes and option price formulas. International Journal of Stochastic Analysis. 2010(347105)

15.      Islam M. S. and Gora P.(2010). Smoothness of density function for random maps. Dyn. Continuous and Discrete Impulsive Systems.17(2)

16.      Islam M. S.(2009). Invariant measures for higher dimensional Markov switching position dependent random maps. International Journal of Bifurcation and Chaos. 19(1): 409-417.

17.      Islam, M. S. (2007), Piecewise linear probability density functions of invariant measures for position dependent random maps: Global Journal of Pure and Applied Mathematics, Volume 3,

18.      Islam, M. S., Gora, P. and Boyarsky, A. (2006), Invariant densities of random maps have lower bounds on their supports: J. Appl. Math. Stoch. Anal. 2006, Art. ID 79175, 13 pp.

19.      Góra, P., Boyarsky, A., Islam, M. S. and Bahsoun, W. (2006), Absolutely continuous invariant measures that cannot be observed experimentally: SIAM J. Appl. Dyn. Syst. 5, no. 1, 84-90.

20.      Islam,M. S (2006), Absolutely continuous invariant measures of linear interval maps: Int. J. Pure Appl. Math. 27, no. 4, 449 - 464.

21.      Islam, M. S., Gora, P., Boyarsky, A. (2005), Approximation of absolutely continuous invariant measures for Markov switching position dependent random maps.: Int. J. Pure Appl. Math. 25, no. 1, 51-78.

22.      Islam, M. S., Gora, P., Boyarsky, A. (2005) A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps: J. Appl. Math. Stoch. Anal., no. 2, 133-141.

23.      Boyarsky, A., Góra, P.; Islam, M. S. (2005), Randomly chosen chaotic maps can give rise to nearly ordered behavior: Phys. D 210, no. 3-4, 284-29.