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An estimate of Burkholder type for stochastic processes defined by the stochastic integral. (English) Zbl 0539.60056
A one-sided Burkholder type inequality with $$p\geq 2$$ is proved for a stochastic convolution integral on a separable Hilbert space H under the assumption that the underlying semigroup S(t) satisfies the estimate (in the operator norm) $$\| S(t)\|_{L(H)}=e^{\alpha t}$$ for some $$\alpha\geq 0.$$
For $$p=2$$ this inequality was independently obtained by the reviewer (using more general integrators and stopping times) and applied to the solution of a class of stochastic evolution equations [submitted to Rep., Forschungsschwerpunkt Dyn. Syst., and Stochastic Anal. Appl. 2(3), 245- 265 (1984)].
Reviewer: P.Kotelenez

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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##### References:
 [1] Da Prato G., Boll. UMI 16 pp 168– (1979) [2] Dellacherie C., Probabilités et potentiel (1975) [3] Ichikawa A., Semilinear Stochastic Evolution Equations: Markov Property and Stability · Zbl 0538.60068 [4] Ikeda N., Stochastic Differential Equations and Diffusion Processes (1981) · Zbl 0495.60005 [5] Kotelenez P., Law of large numbers and central limit theorem for chemical reactions with diffusion (1982) · Zbl 0523.60078 [6] Kotelenez P., A Stopped Doob Inequality for Stochastic Convolution Integrals and Stochastic Evolution Equations (1983) · Zbl 0552.60058
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