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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
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...
Two switching multiple disorder problems for Brownian motions
Multiple disorder problem optimal switching problem Brownian motion
2010/11/8
The multiple disorder problem seeks to determine a sequence of stopping times which are as close as possible to the unknown times of disorders at which the observation process changes its probability ...
Extreme values of derivatives of smoothed fractional Brownian motions
Extreme values of derivatives smoothed fractional Brownian motions
2009/9/22
Let B,(.) be a fractional Brownian motion on R
with parameter 1/2 < H < 1, and consider its smoothed version
b;Hj K((t- sj/b,)BH(s) ds, teR, where the kernel K ( . ) is a density function
and the b...
ON BESOV REGULARITY OF BROWNIAN MOTIONS IN INFINITE DIMENSIONS
Gaussian random variable maximal estimates Besov–Orlicz norm non-separable Banach space
2009/9/18
We extend to the vector-valued situation some earlier work
of Ciesielski and Roynette on the Besov regularity of the paths of the classical
Brownian motion.We also consider a Brownian motion as a Be...
Weak Convergence of Reflected Brownian Motions
Brownian Motions Convergence mild technical assumptions
2009/5/8
We show that if a sequence of domains $D_k$ increases to a domain $D$ then the reflected Brownian motions in $D_k$'s converge to the reflected Brownian motion in $D$, under mild technical assumptions....
We give another proof of the following result from a joint paper with Bálint Tóth: A Brownian motion reflected on an independent time-reversed Brownian motion is a Brownian motion.
Sharp Bounds for Green and Jumping Functions of Subordinate Killed Brownian Motions
Killed Brownian motion, subordinator, Green function, Dirichlet form, jumping function
2009/4/28
In this paper we obtain sharp bounds for the Green function and jumping function of a subordinate killed Brownian motion in a bounded $C^{1,1}$ domain, where the subordinating process is a subordinato...
Entropy Estimate for k-Monotone Functions via Small Ball Probability of Integrated Brownian Motions
Metric entropy class of distribution functions
2009/3/19
Metric entropy of the class of probability distribution functions on [0,1] with a k-monotone density is studied through its connection with the small ball probability of k-times integrated Brownian mo...
