Multiplicative Stochastic Processes Involving the Time-Derivative of a Markov Process.
STATE UNIV OF NEW YORK AT BUFFALO DEPT OF CHEMISTRY
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The characteristic functional of the derivative phit of a Markov process phit and the related multiplicative process sigmat, which obeys the stochastic differential equation isigmat A phitBsigmat, have been studied. Exact equations for the marginal characteristic functional and the marginal average of sigmat are derived. The first equation is applied to obtain a set of equations for the marginal moments of phit in terms of the prescribed properties of phit. It is illustrated by an example how these equations can be solved, and it is shown in general that phit is delta-correlated, with a smooth background. The equation of motion for the marginal average of sigmat is solved for various cases, and it is shown how closed-form analytical expressions for the average sigmat can be obtained. Author
- Statistics and Probability