Optimal Sequential Change Detection for Fractional Diffusion-Type Processes
Keyword(s):
The problem of detecting an abrupt change in the distribution of an arbitrary, sequentially observed, continuous-path stochastic process is considered and the optimality of the CUSUM test is established with respect to a modified version of Lorden's criterion. We apply this result to the case that a random drift emerges in a fractional Brownian motion and we show that the CUSUM test optimizes Lorden's original criterion when a fractional Brownian motion with Hurst index H adopts a polynomial drift term with exponent H+1/2.
2013 ◽
Vol 50
(01)
◽
pp. 29-41
◽
Keyword(s):
Keyword(s):
2014 ◽
Vol 51
(1)
◽
pp. 1-18
◽
2017 ◽
Vol 54
(2)
◽
pp. 444-461
◽
Keyword(s):
2019 ◽
Vol 33
(3)
◽
pp. 1691-1714
◽