Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus

Released on by Jörg-Uwe Löbus
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  • Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus Book Detail

  • Author : Jörg-Uwe Löbus
  • Release Date : 2017-09-25
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 148
  • ISBN 13 : 147042603X
  • File Size : 14,14 MB
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Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus by Jörg-Uwe Löbus PDF Summary

Book Description: The text is concerned with a class of two-sided stochastic processes of the form . Here is a two-sided Brownian motion with random initial data at time zero and is a function of . Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when is a jump process. Absolute continuity of under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, , and on with we verify i.e. where the product is taken over all coordinates. Here is the divergence of with respect to the initial position. Crucial for this is the temporal homogeneity of in the sense that , , where is the trajectory taking the constant value . By means of such a density, partial integration relative to a generator type operator of the process is established. Relative compactness of sequences of such processes is established.

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