On stochastic equations with respect to semimartingales I.†
作者:
I. Gyöngy,
N. V. Krylov,
期刊:
Stochastics
(Taylor Available online 1980)
卷期:
Volume 4,
issue 1
页码: 1-21
ISSN:0090-9491
年代: 1980
DOI:10.1080/03610918008833154
出版商: Gordon and Breach Science Publishers, Inc
数据来源: Taylor
摘要:
Two types of equations are considered:where A is a predictable increasing process, M is a locally square integrable martingale taking values in a Hilbert space, q is a stochastic martingale measure, a,b,c are random functions continuous in x which satisfy natural measurability properties, a kind of monotonity condition and a condition on growth in x. (Thaese are weaker than the usual Lipschitz condition and the condition of linear growth in x, respectively.) A uniqueness and exixtence theorem is proved for the solutions (which take values in Rd) of Eq. (1). It is shown that Eq. (2) Can be rewritten into the form of Eq.(1), and so the uniqueness and existence theorem is obtained for Eq.(2) as well. Further, the dependence of the solutions on parameters and initial values are investigated. The proffs are elementary and are based on the methods used in [8].
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