In this paper, we discuss about the boundedness and convergence analysis of the fractional Brownian motion (FBM) with Hurst parameter H. By the simple analysis and using the mean value theorem for stochastic integrals we conclude that in case of decreasing diffusion function, the solution of FBM is bounded for any H ∈ (0,1). Also, we derive the convergence rate which shows efficiency and accuracy of the computed solutions.
@article{38313,
title = {Boundedness and convergence analysis of stochastic differential equations with Hurst Brownian motion},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i5.38313},
language = {EN},
url = {http://dml.mathdoc.fr/item/38313}
}
Ahmadian, Davood; Rouz, Omid Farkhondeh. Boundedness and convergence analysis of stochastic differential equations with Hurst Brownian motion. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i5.38313. http://gdmltest.u-ga.fr/item/38313/