8,052 research outputs found
Stochastic Averaging Principle for Dynamical Systems with Fractional Brownian Motion
Stochastic averaging for a class of stochastic differential equations (SDEs)
with fractional Brownian motion, of the Hurst parameter H in the interval (1/2,
1), is investigated. An averaged SDE for the original SDE is proposed, and
their solutions are quantitatively compared. It is shown that the solution of
the averaged SDE converges to that of the original SDE in the sense of mean
square and also in probability. It is further demonstrated that a similar
averaging principle holds for SDEs under stochastic integral of pathwise
backward and forward types. Two examples are presented and numerical
simulations are carried out to illustrate the averaging principle
Friedmann cosmology on codimension 2 brane with time dependent tension
A solution of codimension 2 brane is found for which 4 dimensional Friedmann
cosmology is recovered on the brane with time dependent tension, in the
Einstein frame. The effective parameter of equation of state on the
brane can be quintessence like, de Sitter like or phantom like, depending on
integration constants of the solution.Comment: 6 pages, 4 figure
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