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Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient
2020
Mathematics
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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
doi:10.3390/math9010018
fatcat:z3iobuk3ybexpmrz72miah2yvq