We consider reflected backward stochastic differential equations with time and space dependent coefficients in an orthant, and with oblique reflection. Existence and uniqueness of solution are established assuming local Lipschitz continuity of the drift, Lipschitz continuity and uniform spectral radius conditions on the reflection matrix.
We study the limit behaviour of the solution {y^ : 0 < t < ε" 1 } of the multivalued It 's stochastic differential equationwhere -Λ is a multivalued maximal monotone operator and {£/> : t > 0} is astrictly stationary ergodic process independent of the Brownian motion W. More precisely, we prove that {l/t * 0 < £ < ε" 1 } has the same limit behaviour s the solution of an analogous equation obtained by averaging out over the interval [Ο,ε" 1 ] the fluctuations in the drift term arising from the process ζ. Our result can be applied to stochastic differential equations with reflecting boundary conditions or(and) with irregul r drift. When A ΞΞ 0, we obtain the result of Liptser and Stoyanov(1990).Brought to you by |
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