Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times

Antoine Ayache; Narn-Rueih Shieh; Yimin Xiao

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Displaying similar documents to “Multiparameter multifractional brownian motion : local nondeterminism and joint continuity of the local times”

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Let (, ) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process (, )−(0, ) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.

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We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function (), ≥0, consider the measures obtained by conditioning a brownian path so that ≤(), for all ≤, where is the local time spent at the origin by time . It is shown that the measures are tight, and that any weak limit of as →∞ is transient provided that −3/2() is integrable. We conjecture...

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Let ={ (), ∈ℝ } be an (, )-fractional brownian sheet with index =( , …, )∈(0, 1) defined by ()=( (), …, ()) (∈ℝ ), where , …, are independent copies of a real-valued fractional brownian sheet . We prove that if <∑ ...

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We consider exponential functionals of a brownian motion with drift in ℝ, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on...