On approximation of stochastic integral equations driven by continuous p-semimartingales by Kęstutis Kubilius

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On approximation of stochastic integrals with respect to a fractional Brownian motion by Kęstutis Kubilius

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Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations by Fahad Alsharari, Raouf Fakhfakh, Omar Kahouli, Abdellatif Ben Makhlouf

“…This paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic integral equations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs) using the Banach fixed point theorem (BFPT). …”
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Fractional Brownian Motion for a System of Fuzzy Fractional Stochastic Differential Equation by Kinda Abuasbeh, Ramsha Shafqat

“…Under various assumptions regarding the coefficients, we investigate the existence-uniqueness of the solution using an approximation method to the fractional stochastic integral. We can solve an equation with linear coefficients, for example, in financial models Application to a model of population dynamics is also illustrated. …”
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Triangular Function Method is Adopted to Solve Nonlinear Stochastic It o^–Volterra Integral Equations by Guo Jiang, Dan Chen, Fugang Liu

“…Integral operator matrixes of triangular functions are used to convert the nonlinear stochastic integral equations into a system of algebraic equations. …”
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Some Random Fixed-Point Theorems for Weakly Contractive Random Operators in a Separable Banach Space by Kenza Benkirane, Abderrahim EL Adraoui, El Miloudi Marhrani

“…Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.…”
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Generalizing the Black and Scholes Equation Assuming Differentiable Noise by Kjell Hausken, John F. Moxnes

“…This article develops probability equations for an asset value through time, assuming continuous correlated differentiable Gaussian distributed noise. Ito’s (1944) stochastic integral and a generalized Novikov’s (1919) theorem are used. …”
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Relationships among transforms, convolutions, and first variations by Jeong Gyoo Kim, Jung Won Ko, Chull Park, David Skoug

“…In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionals F on Wiener space of the form F(x)=f(〈α1,x〉,…,〈αn,x〉),                                                      (*) where 〈αj,x〉 denotes the Paley-Wiener-Zygmund stochastic integral ∫0Tαj(t)dx(t).…”
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Random Dynamics of the Stochastic Boussinesq Equations Driven by Lévy Noises by Jianhua Huang, Yuhong Li, Jinqiao Duan

“…Some fundamental properties of a subordinator Lévy process and the stochastic integral with respect to a Lévy process are discussed, and then the existence, uniqueness, regularity, and the random dynamical system generated by the stochastic Boussinesq equations are established. …”
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The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method by Yousef Alnafisah

“…Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. …”
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An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion by Yong Xu, Bin Pei, Yongge Li

“…An averaging principle for a class of stochastic differential delay equations (SDDEs) driven by fractional Brownian motion (fBm) with Hurst parameter in (1/2,1) is considered, where stochastic integration is convolved as the path integrals. …”
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Integration by Parts and Martingale Representation for a Markov Chain by Tak Kuen Siu

“…New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integration-by-parts formulas. …”
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