• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.471-480
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• 1996

Consider a strong Markov process $X^0$ that has continuous sample paths in the closed cone $\bar{G}$ in $R^d(d \geq 3)$ such that the process behaves like a ordinary Brownian motion in the interior of the cone, reflects instantaneously from the boundary of the cone and is absorbed at the vertex of the cone. It is shown that $X^0(t)$ has a representation $R(t) \ominus (t)$ where $R(t) \in [0, \infty)$ and $\ominus(t) \in S^{d-1}$, the surface of the unit ball.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1305-1314
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• 2010

In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations driven by a Brownian motion and the martingales of Teugels associated with an independent L$\acute{e}$vy process having a stochastic Lipschitz coefficient. We derive the existence and uniqueness of solutions for these equations via Snell envelope and the fixed point theorem.