# Znanstveni kolokviji

## Stable convergence in law and local asymptotic mixed normality of AMLE of drift parameters in diffusion model

 Vrijeme: 24.2.202117:30 Predavaonica: vir Predavač: Snježana Lubura Strunjak, PMF-MO Naziv: Stable convergence in law and local asymptotic mixed normality of AMLE of drift parameters in diffusion model Opis: The talk is scheduled in virtual setting, using Zoom platform. The talk will also be live-streamed via YouTube. During the meeting, the questions can be posed via chat or audio for participants in the meeting. Everybody interested is invited to participate in the Zoom meeting, with the limit of 100 participants, or to follow the live-broadcast. Link to Zoom meeting will be put here two days before the talk. https://us02web.zoom.us/j/89770176473 Meeting ID: 897 7017 6473 Link to YouTube live broadcast will be put here 10 minutes before the talk. http://www.youtube.com/watch?v=8rItogQJD3A The talk will be in English. Abstract: Stable convergence in law has many applications in showing the asymptotic behaviour of estimators of parameters of stochastic processes. Let $X$ be a diffusion which satisfies a stochastic differential equation of the form: $dX_t=mu(X_t,theta)dt+sigma_0*nu(X_t)dW_t$, where drift parameter $theta$ is unknown and diffusion coefficient parameter $sigma_0$ is known. We have discrete observations $(X_{t_i},0<= i<= n)$ along fixed time interval $[0,T]$. Let bar($theta_n$) be approximate maximum likelihood estimator of drift parameter obtained from discrete observations and let hat($theta$) be maximum likelihood estimator obtained from continuous observations $(X_t,0<= t<= T)$ along fixed time interval $[0,T]$. We proved that bar($theta_n$), when $Delta_n =max_{1<=i<= n}(t_i-t_{i-1})$ tends to zero, is locally asymptotic mixed normal, with covariance matrix which depends on MLE hat($theta$) and on path $(X_t,0<= t<= T)$.

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