A veraging principle for multivalued stochastic differential equations

Abstract

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 |

Stochastic averaging for non-Lipschitz multi-valued stochastic differential equations driven by G-Brownian motion

“…Let σ = 0 and ∂ϕ = A (A is a multi-valued maximal montone operator) in Eq. ( 1), Ngoran and Modeste [4] studied the averaging principle of MSDEs driven by Brownian motion. Xu and Liu [5] removed the integrability condition about the multi-valued maximal montone operator in [4] and obtained the convergence result between the averaged MSDE and the original one.…”

“…( 1), Ngoran and Modeste [4] studied the averaging principle of MSDEs driven by Brownian motion. Xu and Liu [5] removed the integrability condition about the multi-valued maximal montone operator in [4] and obtained the convergence result between the averaged MSDE and the original one. Very recently, Guo and Pei [6] established an averaging principle for MSDEs driven by Poisson point processes.…”

Multivalued Impulsive SDEs Driven by G‐Brownian Noise: Periodic Averaging Result

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Averaging Principle for Backward Stochastic Differential Equations

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