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Stochastic Volterra Equation a Generalization of Fractional Differential Equation

Kiyanpour, Mojtaba | 2022

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54924 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Zohori Zangeneh, Bijan; Jahanipur, Rohollah
  7. Abstract:
  8. 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
  9. Keywords:
  10. 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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