Isolated singularities in the heat equation behaving like fractional Brownian motions
نویسندگان
چکیده
منابع مشابه
Are fractional Brownian motions predictable?
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. Mathematics Subject Classification (2000). Primary 60G07; Secondary 60G15, 60G48, 60G25.
متن کامل9 Are fractional Brownian motions predictable ?
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. 1 Intoduction The question in the title is provocative, of course. Everybody familiar with the theory of stochast...
متن کاملPropagation of Singularities in the Semi-Fractional Brownian Sheet
Let X be a semi-fractional Brownian sheet, that is a centred and continuous Gaussian random field with E[X(s, t)X(ŝ, t̂ )] = (t∧ t̂ )(sα+ ŝα−|s− ŝ|α)/2. We provide, for α ∈ (0, 2), an analysis of the propagation of singularities into the fractional direction of X. Here, singularities are times where the law of the iterated logarithm fails, such as fast points.
متن کاملTaylor expansion for the solution of a stochastic differential equation driven by fractional Brownian motions
We study the Taylor expansion for the solution of a differential equation driven by a multi-dimensional Hölder path with exponent β > 1/2. We derive a convergence criterion that enables us to write the solution as an infinite sum of iterated integrals on a nonempty interval. We apply our deterministic results to stochastic differential equations driven by fractional Brownian motions with Hurst ...
متن کاملThe Fractional Langevin Equation: Brownian Motion Revisited
It is well known that the concept of diffusion is associated with random motion of particles in space, usually denoted as Brownian motion, see e.g. [1-3]. Diffusion is considered normal when the mean squared displacement of the particle during a time interval becomes, for sufficiently long intervals, a linear function of it. When this linearity breaks down, degenerating in a power law with expo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2021.125322