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

DOI: 10.4236/am.2013.41023   PDF   HTML   XML   2,613 Downloads   4,056 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

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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