44,355 research outputs found
Hawking radiation from the cosmological horizon in a FRW universe
It is well known that there is a Hawking radiation from the cosmological
horizon of the de-sitter spacetime, and the de-sitter spacetime can be a
special case of a FRW universe. Therefore, there may be a corresponding Hawking
radiation in a FRW universe. Indeed, there have been several clues showing that
there is a Hawking radiation from the apparent horizon of a FRW universe. In
our paper, however, we find that the Hawking radiation may come from the
cosmological horizon. Moreover, we also find that the Hawking radiation from
the apparent horizon of a FRW universe in some previous works can be a special
case in our result, and the condition is that the variation rate of
cosmological horizon is zero. Note that, this condition is
also consistent with the underlying integrable condition in these works from
the apparent horizon.Comment: V3: 12 pages, no figure, typos corrected, new references added,
version shorted and accepted by PL
Properties of solutions of stochastic differential equations driven by the G-Brownian motion
In this paper, we study the differentiability of solutions of stochastic
differential equations driven by the -Brownian motion with respect to the
initial data and the parameter. In addition, the stability of solutions of
stochastic differential equations driven by the -Brownian motion is
obtained
Local time and Tanaka formula for G-Brownian Motion
In this paper, we study the notion of local time and Tanaka formula for the
G-Brownian motion. Moreover, the joint continuity of the local time of the
G-Brownian motion is obtained and its quadratic variation is proven. As an
application, we generalize It^o's formula with respect to the G-Brownian motion
to convex functions.Comment: 29 pages, "Finance and Insurance-Stochastic Analysis and Practical
Methods", Jena, March 06,200
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