Simultaneous Determination of the Drift and Diffusion Coefficients in Stochastic Differential Equations

  • [2017-04-13]

    Speaker:Cristofol Michel    Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Time:2017-4-12  15:00-16:00 

    Place:Room 1518, School of Mathematical Sciences



       In this talk, I consider a one-dimensional Itoˆ diffusion process $X_t$ with possibly nonlinear drift and diffusion coefficients. I will show that, when the diffusion coefficient is known, the drift coefficient is uniquely determined by an observation of the expectation of the process during a small time interval, and starting from values $X_0$ in a given subset of $. With the same type of observation, and given the drift coefficient, I also show that the diffusion coefficient is uniquely determined. When both coefficients are unknown, they are simultaneously uniquely determined by the observation of the expectation and variance of the process, during a small time interval, and starting again from values $X_0$ in a given subset of $.



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