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Abstract Volterra equations with stochastic kernels. (English. Ukrainian original) Zbl 0998.60054

Theory Probab. Math. Stat. 64, 139-151 (2002); translation from Teor. Jmovirn. Mat. Stat. 64, 118-128 (2001).
The Volterra equation \[ x(t,\omega)=f(t,\omega)+\int_0^t a(t-s,\omega)Ax(s,\omega)ds \] with the stochastic kernel \(a(t,\omega)\) is considered. The author proposes a sufficient condition for existence and uniqueness of a solution to this equation. As application, an equation from fluid mechanics is investigated.

MSC:

60H05 Stochastic integrals
76M35 Stochastic analysis applied to problems in fluid mechanics
60H07 Stochastic calculus of variations and the Malliavin calculus
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