Researcher:
İyigünler, İsmail

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Master Student

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İsmail

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İyigünler

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İyigünler, İsmail

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2007 - 200922010 - 20121

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Researcher Of Publications: search.filters.isAuthorOfPublication.33f63bee-6890-453c-b371-204a7017b456

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    Exact linearization of one-dimensional jump-diffusion stochastic differential equations
    (Springer, 2008) Ünal, Gazanfer; Sanver, Abdullah; N/A; İyigünler, İsmail; Master Student; Graduate School of Sciences and Engineering; N/A
    Necessary and sufficient conditions for the linearization of the one-dimensional Ito jump-diffusion stochastic differential equations (JDSDE) are given. Stochastic integrating factor has been introduced to solve the linear JDSDEs. Exact solutions to some linearizable JDSDEs have been provided.
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    Linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations
    (World Scientific Publ Co Pte Ltd, 2007) Unal, Gazanfer; Khalique, C. Masood; N/A; İyigünler, İsmail; Master Student; Graduate School of Sciences and Engineering; N/A
    Necessary and sufficient conditions for the linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations are given. Stochastic integrating factor is introduced to solve the linear jump-diffusion stochastic differential equations. Closed form solutions to certain linearizable jump-diffusion stochastic differential equations are obtained.
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    PublicationOpen Access
    Exact solvability of stochastic differential equations driven by finite activity levy processes
    (Multidisciplinary Digital Publishing Institute (MDPI), 2012) Ünal G.; Department of Mathematics; İyigünler, İsmail; Çağlar, Mine; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 105131
    We consider linearizing transformations of the one-dimensional nonlinear stochastic differential equations driven by Wiener and compound Poisson processes, namely finite activity Levy processes. We present linearizability criteria and derive the required transformations. We use a stochastic integrating factor method to solve the linearized equations and provide closed-form solutions. We apply our method to a number ofstochastic differential equations including Cox-Ingersoll-Ross short-term interest rate model, log-mean reverting asset pricing model and geometric Ornstein- Uhlenbeck equation all with additional jump terms. We use their analytical solutions to illustrate the accuracy of the numerical approximations obtained from Euler and Maghsoodi discretization schemes. The means of the solutions are estimated through Monte Carlo method.