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Integral representations and properties of operator fractional Brownian motions
dichotomy principle integral representations long-range dependence multivariate Brownian motion operator fractional Brownian motion operator self-similarity
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2011/3/18
Operator fractional Brownian motions (OFBMs) are (i) Gaussian, (ii) operator self-similar and (iii) stationary increment processes. They are the natural multivariate generalizations of the well-studie...
Positivity of Brownian Transition Densities
Transition Densities Brownian Motion Eigenvalue Expansion Fine Topology Regular Points
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2009/5/8
Let $B$ be a Borel subset of $R^d$ and let $p(t,x,y)$ be the transition densities of Brownian motion killed on leaving $B$. Fix $x$ and $y$ in $B$. If $p(t,x,y)$ is positive for one $t$, it is positiv...
Canonical Decompositions of Certain Generalized Brownian Bridges
Brownian motion Brownian bridge Canonical decomposition Volterra transform
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2009/4/29
We define a generalized Brownian bridge and we provide some information about its filtration. Two decompositions of this process as a semi-martingale are given. The first one is a Volterra decompositi...
Boundary Crossings of Brownian Motion
Brownian motion with trend boundary crossing probability large deviations
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2009/4/27
Let B be a standard Brownian motion and let b_gamma be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of P{ B(t)< b_gamma(t), forall tin [0,1]} ...