1993 | OriginalPaper | Chapter
A Definitions and results from stochastic calculus
Author : Dr. Richard Flavell
Published in: Modelling Reality and Personal Modelling
Publisher: Physica-Verlag HD
Included in: Professional Book Archive
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In the discussion above, we have made extensive use of some definitions and results from the theory of stochastic calculus. To disecumber our discussion from these technicalities, we have confined those which are less known in this section. For a more complete treatment see for instance Protter [3], whose notation is followed here. Let (Ω, ℱ, P, {ℱ t }) be a filtered complete probability space satisfying the usual conditions (see [3]). Given a stochastic process X on (Ω, ℱ, P) we write X t instead of X(t, ω) and X t − for lim s↑t X(s, ω). Moreover, we define ΔX t = X t − X t − to be the jump at t. Finally, we set X0− = 0 by convention; remark however that we do not require X0 = 0.