| Title |
Positive solutions of the fractional SDEs with non-Lipschitz diffusion coefficient |
| Authors |
Kubilius, Kęstutis ; Medžiūnas, Aidas |
| DOI |
10.3390/math9010018 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2021, vol. 9, iss. 1, art. no. 18, p. [1-14].. eISSN 2227-7390 |
| Keywords [eng] |
fractional Brownian motion ; backward Euler approximation ; fractional Ait–Sahalia model ; fractional CKLS model ; Hurst index |
| Abstract [eng] |
We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories of the fractional CKLS model with β>1 are not necessarily positive. We obtain the almost sure convergence rate of the backward Euler approximation scheme for solutions of the considered SDEs. We also obtain a strongly consistent and asymptotically normal estimator of the Hurst index H>1/2 for positive solutions of FSDEs. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2021 |
| CC license |
|
