A class of backward stochastic differential equations with discontinuous coefficients

Bsdes on Finite and Infinite Time Horizon With Discontinuous Coefficients

“…If 0 ≤ T < +∞, let u(t), v(t) = A, the result of this paper includes the result of Lepeltier and San Martin [8] and Theorem 3 in [7].…”

“…Owe to the restriction of Lipschitz conditions, many authors improved the results of Pardoux and Peng (see [2,4,6,8,9]). Particularly, Gia [7] obtained the existence of solutions of one dimensional BSDEs with linear growth and discontinuous assumptions.…”

“…Motivated by these works, especially by [7] and [5], we are devoted to solving the one dimensional BSDEs on finite and infinite time horizon with discontinuous conditions and general growth of generator. In Section 2, we give some notations and technical lemmas.…”

Lp solutions of multidimensional BSDEs with weak monotonicity and general growth generators

“…From the beginning, many authors attempted to improve the result of [36] by weakening the Lipschitz hypothesis on g, see [1,2,4,[6][7][8][13][14][15][16][17][18][19][20][22][23][24][26][27][28][29][31][32][33][34][35]37,40,43,45,46], or the L 2 integrability assumptions on ξ, see [5][6][7]11,21,23,38,44], or relaxing the finite terminal time T to a stopping time or infinity, see [12,25,29,34,35,45]. From these results we can see that the case of one-dimensional BSDEs is easier to handle due to the presence of the comparison theorem of solutions (see [6][7][8]…”

“…From these results we can see that the case of one-dimensional BSDEs is easier to handle due to the presence of the comparison theorem of solutions (see [6][7][8]11,12,[17][18][19][20][21]25,[27][28][29]31,32,38]). …”