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An Upper Bound for Conditional Second Moment of the Solution of a SDE

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DOI: 10.4236/am.2013.41023    2,493 Downloads   3,839 Views   Citations

ABSTRACT

Let be a filtration on some probability space and let denote the class of all -adapted -valued stochastic processes M such that for all t>s0 and the process is continuous (the conditional expectations are extended, so we do not demand that . It is shown that each is a locally square integrable martingale w. r. t. . Let X be the strong solution of the equation where , t is a continuous increasing process with -measurable values at all times, and Q is an -valued random function on , continuous in and -progressive at fixed x. Suppose also that there exists an -measurable in nonnegative random process Ψ such that, for all

Then where

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. Yurachkivsky, "An Upper Bound for Conditional Second Moment of the Solution of a SDE," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 135-143. doi: 10.4236/am.2013.41023.

References

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