Geodesic
On boundary conditions for stochastic evolution equations with an extremally chaotic source
Sbornik. Mathematics, Tome 186 (1995) no. 12, pp. 1693-1709 
S. A. Albeverio; T. J. Lyons; Yu. A. Rozanov. On boundary conditions for stochastic evolution equations with an extremally chaotic source. Sbornik. Mathematics, Tome 186 (1995) no. 12, pp. 1693-1709. http://geodesic.mathdoc.fr/item/SM_1995_186_12_a0/
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     title = {On boundary conditions for stochastic evolution equations with an~extremally chaotic source},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Stochastic differential equation of the form $$ d\xi_t=A\xi_t\,dt+Bd\eta_t^0, \qquad t\in I=(t_0,t_1), $$ are considered for a generalized random field $$ \xi_t\equiv(\varphi,\xi_t), \quad \varphi\in C_0^\infty(G), $$ in the domain $G\subseteq\mathbb R^d$ with stochastic boundary conditions on the boundary corresponding to an operator $A\leqslant0$ and an extremal operator coefficient $B$ (strengthening the chaotic source $d\eta^0_t$ of ‘white noise’ type).

[1] Albeverio S., Rozanov Yu. A., “O stokhasticheskikh evolyutsionnykh uravneniyakh so stokhasticheskimi granichnymi usloviyami”, Teoriya veroyatn. i ee prim., 38:1 (1993) | MR | Zbl

[2] Rozanov Yu. A., “Stokhasticheskie sobolevskie prostranstva i ikh granichnyi sled”, Teoriya veroyatn. i ee prim., 40:1 (1995), 111–124 | MR | Zbl

[3] Rozovskii B. L., Stochastic Evolution Systems, Kluwer, 1990 | MR | Zbl

[4] Walsh I., “An introduction to stochastic partial differential equations”, Ecole d'Ete de Saint Flon XIV, Lect. Notes Math., 1180, 1986 | Zbl