Speaker：Cristofol Michel
Aix Marseille
Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Time：2017412 15:0016:00
Place：Room 1518, School of Mathematical Sciences
Detail：
In this talk, I consider a
onedimensional Itoˆ diﬀusion process $X_t$ with possibly nonlinear
drift and diﬀusion coeﬃcients. I will show that, when the diﬀusion coeﬃcient is known, the drift coeﬃcient is uniquely determined by an
observation of the expectation of the process during a small time interval, and
starting from values $X_0$ in a given subset of ${\mathbb R}$. With the same
type of observation, and given the drift coeﬃcient, I also show that the diﬀusion coeﬃcient is uniquely determined. When both
coeﬃcients are
unknown, they are simultaneously uniquely determined by the observation of the
expectation and variance of the process, during a small time interval, and
starting again from values $X_0$ in a given subset of ${\mathbb R}$.
