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حل معادله ولترای تصادفی تعمیمی از مشتق کسری
کیان پور، مجتبی Kiyanpour, Mojtaba
Stochastic Volterra Equation a Generalization of Fractional Differential Equation
Kiyanpour, Mojtaba | 2022
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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 54924 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Zohori Zangeneh, Bijan; Jahanipur, Rohollah
- Abstract:
- We establish the existence and uniqueness of the mild solution for stochastic Volterra equation with a non-self-adjoint operator. The specific Volterra equation that we consider is a generalization of the fractional differential equation. To obtain the mild solution for the case of multiplicative problem, the resolvent property of the linear perturbation of a sectorial operator will be considered. Moreover, we establish the existence and uniqueness of the mild solution for semilinear stochastic Volterra equation involving a demicontinuous and semimonotone nonlinearity. The Volterra equation in this case, has a positive-type memory kernel. To obtain the mild solution of the multiplicative problem, we use the Itô-type inequality and an inequality concerning stochastic convolution. We prove also that the mild solution is continuous with respect to initial conditions and coefficients
- Keywords:
- Stochastic Partial Differential Equation ; Gaussian Noise ; Multiplicative Noise ; Monotone Operators ; Stochastic Q-Wiener Process ; Perturbation Theory ; Volterra Differential Equation ; Non-Selfadjoint Operator
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