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