Abstract
In this paper, we study the existence theorem for L^{p} (1<p<2) solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for L^{p} (1<p<2) solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704–718, 2013).
Highlights
The theory of nonlinear backward stochastic differential equations (BSDEs for short) was developed by Pardoux and Peng (1990), from which we know that there exists a unique adapted and square integrable solution to a BSDE of the typeT yt = ξ + g(s, ys, zs)ds − zsdWs, t ∈ [0, T ], (1)t t provided the function g is Lipschitz in both variables y and z, and ξ and (g(t, 0, 0))0≤t≤T are square integrable
We study the existence theorem for Lp (1 < p < 2) solutions to a class of 1-dimensional infinite time interval BSDEs under the conditions that the coefficients are continuous and have linear growths
We study the existence and uniqueness theorem for Lp (1 < p < 2) solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients
Summary
In Lepeltier and San Martin (1997), the authors got the existence of a solution for a 1-dimensional BSDE where the coefficient We study the existence and uniqueness theorem for Lp (1 < p < 2) solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients.
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