Articlebronze2003

Small-diffusion asymptotics for discretely sampled stochastic differential equations

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Stochastic processes and financial applications Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

1051-1069: The minimum-contrast estimation of drift and diffusion coefficient parameters for a multi-dimensional diffusion process with a small dispersion parameter $\varepsilon$ based on a Gaussian approximation to transition density is presented when the sample path is observed at equidistant times $k/n$, $k=0,1,\rm \dots,n$. We study asymptotic results for the minimum-contrast estimator as $\varepsilon$ goes to $0$ and $n$ goes to $\infty$ simultaneously.

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References

1983Stochastic Differential Equations and Diffusion Processes 1993Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes 1997Estimation of an Ergodic Diffusion from Discrete Observations 1995Martingale Estimation Functions for Discretely Observed Diffusion Processes 1992Estimation for diffusion processes from discrete observation 1989Approximate discrete-time schemes for statistics of diffusion processes 1986Estimation of the coefficients of a diffusion from discrete observations 1993On the estimation of the diffusion coefficient for multi-dimensional diffusion processes

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2008Estimation for stochastic differential equations with a small diffusion coefficient 2012Estimating functions for diffusion-type processes 2009Least squares estimator for discretely observed Ornstein–Uhlenbeck processes with small Lévy noises 2004Estimation for Discretely Observed Small Diffusions Based on Approximate Martingale Estimating Functions 2004Asymptotic Expansion for Small Diffusions Applied to Option Pricing

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