Geodesic
Solution of nonlinear stochastic equations with a~generator of a~semigroup discontinuous at zero
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 90-99

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In this paper we study the Cauchy problem for a nonlinear stochastic equation with a generator of a semigroup discontinuous at zero. We prove the unique existence of a mild solution for some class of such semigroups. We establish a connection between weak and mild solutions for such semigroups.
Keywords: abstract stochastic Cauchy problem, operator semigroup, $Q$-Wiener process, stochastic integral. 
@article{IVM_2011_6_a10,
     author = {A. A. Ogorodnikov},
     title = {Solution of nonlinear stochastic equations with a~generator of a~semigroup discontinuous at zero},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {90--99},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a10/}
}
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A. A. Ogorodnikov. Solution of nonlinear stochastic equations with a~generator of a~semigroup discontinuous at zero. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 90-99. http://geodesic.mathdoc.fr/item/IVM_2011_6_a10/