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Deconvolution with unknown error distribution
Deconvolution Fourier transform kernel estimation spectralcut off Sobolev space source condition optimal rate of convergence
2010/4/29
We assume that an additional sample x1, . . . , xm from fx is observed.
Estimators of fX and its derivatives are constructed by using nonparametric
estimators of fY and fx and by applying a spectral...
The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential
Standard Brownian Excursions Brownian Bridges Ring Polymers End-Attached Polymers
2009/5/8
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark...
Perfect Simulation from the Quicksort Limit Distribution
Quicksort random variate generation simulation perfect simulation rejection method fixed-point equation
2009/5/4
The weak limit of the normalized number of comparisons needed by the Quicksort algorithm to sort n randomly permuted items is known to be determined implicitly by a distributional point equation. We g...
A Bound for the Distribution of the Hitting Time of Arbitrary Sets by Random Walk
Random walk hitting time exit time sandpile model
2009/4/28
We consider a random walk $S_n = sum_{i=1}^n X_i$ with i.i.d. $X_i$. We assume that the $X_i$ take values in $Bbb Z^d$, have bounded support and zero mean. For $A subset Bbb Z^d, A ne emptyset$ we def...
Acknowledgment of Priority: When Does a Randomly Weighted Self-normalized Sum Converge in Distribution? (Elect. Comm. in Probab. 10 (2005), 70--81)
Domain of attraction selfCnormalize sums regular variation
2009/4/27
Christian Houdre has kindly pointed us to a paper by A. Fuks, A. Joffe and J. Teugels, where their Theorem 5.3 is our Proposition 3 in the case 0
When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
Domain of attraction selfCnormalize sums regular variation
2009/4/24
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
The Redundancy of a Computable Code on a Noncomputable Distribution
Redundancy Computable Code Noncomputable Distribution
2010/3/17
We introduce new definitions of universal and
superuniversal computable codes, which are based on a code’s
ability to approximate Kolmogorov complexity within the prescribed
margin for all individu...
When Does a Randomly Weighted Self-normalized Sum Converge in Distribution?
Weighted Self-normalized Sum Distribution
2009/4/7
We determine exactly when a certain randomly weighted, self--normalized sum converges in distribution, partially verifying a 1965 conjecture of Leo Breiman. We, then, apply our results to characterize...
Degree distribution nearby the origin of a preferential attachment graph
preferential attachment graph Degree distribution
2009/3/30
In a 2-parameter scale free model of random graphs it is shown that the asymptotic degree distribution is the same in the neighbourhood of every vertex. This degree distribution is still a power law w...
Asymptotic Distribution of Coordinates on High Dimensional Spheres
Asymptotic Distribution Coordinates Dimensional Sphere
2009/3/27
The coordinates xi of a point x = (x1, x2,..., xn) chosen at random according to a uniform distribution on the l2(n)-sphere of radius n1/2 have approximately a normal distribution when n is large. The...
Degree distribution nearby the origin of a preferential attachment graph
Degree distribution preferential attachment graph
2009/3/23
In a 2-parameter scale free model of random graphs it is shown that the asymptotic degree distribution is the same in the neighbourhood of every vertex. This degree distribution is still a power law w...
Asymptotic Distribution of Coordinates on High Dimensional Spheres
Asymptotic Distribution Coordinates Dimensional Spheres
2009/3/23
The coordinates xi of a point x = (x1, x2,..., xn) chosen at random according to a uniform distribution on the l2(n)-sphere of radius n1/2 have approximately a normal distribution when n is large. The...
Distribution of the Brownian motion on its way to hitting zero
Brownian motion probability density
2009/3/23
For the one-dimensional Brownian motion $B=(Bt)t≥ 0$, started at $x>0$, and the first hitting time $τ=inf{t≥ 0:Bt=0}$, we find the probability density of $Buτ$ for a $uin(0,1)$, i.e. of the Brownian ...
Markov processes with product-form stationary distribution
Markov process stationary distribution
2009/3/23
We consider a continuous time Markov process (X,L), where X jumps between a finite number of states and L is a piecewise linear process with state space Rd. The process L represents an “inert drift” o...
Some Diffusion Processes Associated With Two Parameter Poisson-Dirichlet Distribution and Dirichlet Process
Some Diffusion Processes Two Parameter Poisson-Dirichlet Distribution Dirichlet Process
2010/3/19
The two parameter Poisson-Dirichlet distribution PD( , ) is the distribution
of an infinite dimensional random discrete probability. It is
a generalization of Kingman’s Poisson-Dirichlet distributi...