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Book Sections Year : 2018

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.
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hal-03560886 , version 1 (19-02-2022)

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Michel Cristofol, L Roques. Simultaneous determination of two coefficients in Itô diffusion processes: theoretical and numerical approaches. Springer. Inverse problems and related topics, 310, Springer, 2018, Springer Proceedings in Mathematics & Statistics, 978-981-15-1591-0. ⟨10.1007/978-981-15-1592-7_3⟩. ⟨hal-03560886⟩
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