Generalized BSDEs driven by fractional Brownian motion

Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion

“…Given the widespread applications of the long-range dependence of the fBm and non-Lipschitz SDEs, in this paper, we will make the first attempt to study the stochastic averaging for SDEs driven by fBm with non-Lipschitz coefficients proposed. Let us also point out that, the SDEs driven by fBm could not be treated [3][4][5][6][7][8][9][10][11][12][13][14][15][16] Stochastic averaging principle for SDEs by the method for SDEs driven by Bm. For example, due to the fact that the stochastic integral with respect to fBm is no longer a martingale, we definitely lost good inequalities such as Burkholder-Davis-Gundy inequality which is crucial for SDEs driven by Bm.…”

Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion

“…Moreover, they developed a theory of backward stochastic variational inequalities, that is they proved the existence and uniqueness of the solution of the reflected BSDEs driven by a fBm. The existence and uniqueness of the generalized BSDEs driven by a fBm with Hurst parameter H greater than 1/2 was shown in [13] and in [4] the existence and uniqueness of the generalized backward stochastic variational inequalities driven by a fBm with Hurst parameter H greater than 1/2 was proven.…”

Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion

“…In the last few years, some articles have been published choosing fractional Brownian motion (fBm) as an underlying diffusive process (e.g., Refs. [7][8][9][14][15][16][17] and references therein). For example, Jiang et al [9] proposed a class of stochastic heat equations with first order fractional noises and established the existence and uniqueness of the solution of the equation.…”

“…Xiao et al [17] presented a pricing model for equity warrants in a mixed fractional Brownian environment and proposed a hybrid intelligent algorithm to solve the nonlinear optimization problem. Jańczak-Borkowska [8] investigated the existence and uniqueness of generalized backward stochastic differential equation driven by fBm with Hurst parameter H greater than 1/2, and shown the connection between this solution and the solution of parabolic partial differential equation with Neumann boundary condition. Rostek and Schöbel [14] gave a note on the use of fBm for financial modeling and clarified that fBm is suited for economic modeling.…”