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Stability of some anticipating semilinear stochastic differential equations of Skorohod type

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In the present paper, we study different types of stability of the solution of a semi-linear anticipating stochastic differential equation driven by a Brownian motion, with a random variable as initial condition. The involved stochastic integral is the Skorohod one. Being the initial condition random, we need to redefine the stability concepts. The new stability criteria depend on the derivative of the initial condition in the Malliavin calculus sense.

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Journal of Dynamics and Differential Equations, 2025, Vol. 37, p.1259–1294,

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Stability of some anticipating semilinear stochastic differential equations of Skorohod type