Stochastic differential equations in Hilbert space: Properties of solutions, limit theorems, asymptotic expansions with respect to a small parameter. II. (English. Ukrainian original) Zbl 0958.60058

Mishura, Yu. S.; Lavrent’jev, O. S.

Theory Probab. Math. Stat. 59, 139-147 (1999); translation from Teor. Jmorvirn. Mat. Stat. 59, 135-143 (1998).

[For part I see ibid. 58, 123-137 (1999), resp. ibid. 58, 114-127 (1998; Zbl 0940.60082).]
The authors investigate stochastic differential equations in a Hilbert space with a linear operator valued drift and nonlinear diffusion. Conditions for weak convergence of measures which correspond to solutions of these stochastic differential equations are considered. Also, linear stochastic differential equations in a Hilbert space with parameter \(\varepsilon>0\) are studied. Asymptotic of the first exit time beyond the bound of some region in a Hilbert space for solutions of such perturbed stochastic differential equations is investigated.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05	Stochastic integrals
60G44	Martingales with continuous parameter

Keywords:

stochastic differential equations; Hilbert space; asymptotic expansion; limit theorems; weak compactness of measures

Citations:

Zbl 0940.60082