Naslov
An approximate maximum likelihood estimator of drift parameters in a multidimensional diffusion model

Autori
Huzak, Miljenko ; Lubura Strunjak, Snježana ; Vlahek, Andreja

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, neobjavljeni rad, znanstveni

Skup
7th Croatian Mathematical Congress

Mjesto i datum
Split, Hrvatska, 15.06.2022. - 18.06.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
asymptotic mixed normality, multidimensional model, uniform ellipticity condition

Sažetak
For fixed T, we analyze a k x k-dimensional vector stochastic differential equation over time interval [0, T]: dXt=μ(Xt, θ)dt+ν(Xt)σdWt where μ(Xt, θ) is a k x k-dimensional vector and ν(Xt) is a k x k-dimensional matrix, both consisting of sufficiently smooth functions. (Wt, t≥0) is a k x k-dimensional standard Brownian motion whose components Wt1, Wt2, …, Wtk are independent scalar Brownian motions. Matrix of diffusion parameters σ is known, and vector of drift parameters θ is unknown. We prove that approximate maximum likelihood estimator of drift parameter obtained from discrete observations (XiΔn, 0≤i≤n), when Δn=T/n tends to zero, is locally asymptotic mixed normal with covariance matrix that depends on maximum likelihood estimator obtained from continuous observations (Xt, 0≤t≤T), and on path (Xt, 0≤t≤T). To prove the desired result, we emphasize the importance of the so-called uniform ellipticity condition of diffusion matrix.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA