An estimate of Burkholder type for stochastic processes defined by the stochastic integral. (English) Zbl 0539.60056

Tubaro, L.

Stochastic Anal. Appl. 2, 187-192 (1984).

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)

Keywords:

Burkholder type inequality; stochastic convolution integral; evolution equations

References:

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