Browsing by Author "LALLOUCHE , Abdellah"

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    Mathematical Analysis and Modeling for a Class of Stochastic Differential and Difference Equations
    (Faculty of Sciences, 2024) AOUFI , Amani; LALLOUCHE , Abdellah
    This dissertation has embarked on a comprehensive exploration of various equations, delving deeply into the analysis and application of stochastic differential and difference equations. Our investigation covered a spectrum of equations, focusing particularly on how noise can act as a stabilizing factor. The study of stochastic equations in general needs a full knowledge of probability theory and stochastic calculus including stochastic processes, stochastic integration and stochastic differentiation. After studying stochastic calculus, we briefly discuss an unsolved problem of stabilization by noise for difference equations.
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    On Some Aspects Of Stochastic Differential And difference Equatins And Applications
    (Faculty of Sciences, 2024) TADJINE , Meriem; LALLOUCHE , Abdellah
    This dissertation addresses mathematical notion and the properties concerning stochastic processes and some importante example that we needed to build a irreplaceable concepts and here we are talking about stocastic calculus which depends primarily on Itô calculus including Itô integral and Itô formula, down to one of the most essential points stochastic differential equation, these equation are a generalization of deterministic differential equations that incorporate some randomness into continuous-time systems, and for discrete-time systems we deal with stochastic difference equations, and by integrating stochastic elements, these systems can achieve stability under conditions where deterministic models might fail.