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Keywords:

  • discrete time sampling;
  • inference for diffusion processes;
  • stochastic differential equation

We consider a one-dimensional diffusion process X, with ergodic property, with drift b(x, θ) and diffusion coefficient a(x, σ) depending on unknown parameters θ and σ. We are interested in the joint estimation of (θ, σ). For that purpose, we dispose of a discretized trajectory, observed at n equidistant times tni = ihn, 1 ≤in. We assume that hn[LEFTWARDS ARROW] 0 and nhn[LEFTWARDS ARROW]∞. Under the condition nhnp[LEFTWARDS ARROW] 0 for an arbitrary integer p, we exhibit a contrast dependent on p which provides us with an asymptotically normal and efficient estimator of (θ, σ).