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A note on global solution to stochastic differential equation based on a semimartingale with spatial parameters

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Abstract

We give here some criterions for the existence and uniqueness of a global solution to a stochastic differential equation based on a semimartingale with spatial parameters of the form

$$\varphi _t = x_0 + \smallint _0^t F(\varphi _s ,ds)$$

The criterions are stated in terms of the characteristic of the semimartingale defining the equation. Our results include some cases where Khasminskii's test can not be applied. Several examples are worked out to illustrate our results.

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References

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, England

    Xuerong Mao

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  1. Xuerong Mao
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Mao, X. A note on global solution to stochastic differential equation based on a semimartingale with spatial parameters. J Theor Probab 4, 161–167 (1991). https://doi.org/10.1007/BF01046999

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  • DOI: https://doi.org/10.1007/BF01046999

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