Simultaneous determination of two coefficients in Itô diffusion processes: theoretical and numerical approaches
Abstract
In this paper, we consider a one-dimensional Itô diffusion process X t with possibly nonlinear drift and diffusion coefficients. In a first part, we show that both coefficients are simultaneously uniquely determined by the observation of the expectation and variance of the process, during a small time interval, and starting from any values X 0 in a given subset of R. Then in a second part, we present some numerical simulations which illustrate that this type of observation can be used in practice to estimate the coefficients of a diffusion process.
Domains
Analysis of PDEs [math.AP]
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