Simultaneous determination of two coefficients in Itô diffusion processes: theoretical and numerical approaches

Michel Cristofol (1, 2, 3) , L Roques (4)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université
3 UREC - Unite réseaux du CNRS
4 BioSP - Biostatistique et Processus Spatiaux

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.

Domaines: Equations aux dérivées partielles [math.AP]

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⟩