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Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates
Law of large numbers branching Hunt processes spine approach h-transform spectral gap
2016/1/26
We establish weak and strong law of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure with respect to the underlying Hunt process, and the ...
Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes
Central limit theorem branching Markov process supercritical mar- tingale
2016/1/25
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms sati...
Central Limit Theorems for Supercritical Branching Markov Processes
Central limit theorem branching Markov process supercritical mar- tingale eigenfunction expansion
2016/1/25
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations o...
Small Value Probabilities for Supercritical Branching Processes with Immigration
Supercritical Galton-Watson branching process small value probability immigration
2016/1/25
We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite,strictly...
Multitype Branching Brownian Motion and Traveling Waves
Multitype branching Brownian motion Spine approach Ad- ditive martingale Traveling wave solution
2016/1/25
This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes
Central limit theorem branching Markov process supercritical mar- tingale
2016/1/20
In this paper, we establish a spatial central limit theorem for a large class of supercritical branching, not necessarily symmetric, Markov processes with spatially dependent branching mechanisms sati...
Conditional limit theorems for critical continous-state branching processes
Empirical likelihood high dimensional data analysis independence sure screening large deviation
2016/1/20
In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism ψ(λ) = λ 1+α L(1/λ)where α ∈ [0,1] and L is slowly varying at ∞. We pro...
Central Limit Theorems for Supercritical Branching Markov Processes
Central limit theorem branching Markov process supercritical
2016/1/20
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations o...
Small Value Probabilities for Supercritical Branching Processes with Immigration
Supercritical Galton-Watson branching process small value probability immigration
2016/1/20
We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite,strictly...
Multitype Branching Brownian Motion and Traveling Waves
Multitype branching Brownian motion Spine approach Ad- ditive martingale Traveling wave solution
2016/1/20
This article studies the parabolic system of equations which is closely related to multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this sy...
The Future Has Thicker Tails than the Past: Model Error As Branching Counterfactuals
Fukushima Counterfactual histories Risk management Epistemology of probability Model errors Fragility and Antifragility Fourth Quadrant
2012/11/23
Ex ante forecast outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. Reapplying measurements of uncertainty about the estimation errors...
Branching Markov processes on fragmentation trees generated from the paintbox process
paintbox process Markov processes
2011/7/19
A fragmentation of a set $A$ is a graph with vertices labeled by subsets of $A$ which obey a certain parent-child relationship. A random fragmentation tree is a probability distribution on the space o...
Size-biased branching population measures and the multi-type x\logx condition
general branching process immigration size-biased measure xlogx condition
2010/3/9
We investigate the x log x condition for a general (Crump–Mode–Jagers) multi-type branching
process with a general type space by constructing a size-biased population measure that relates
to the ord...
BCCBJBATllON TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM FINITE VARIANCE BRANCHING SYSTEMS
Functional central limit theorem branching particles systems occupation time fluctuations
2009/9/18
Functional limit theorems are presented for the rescaled
occupation time fluctuation process of a critical finite variance
branching particle system in Rd with symmetric a-stable motion starting
of...
OCCUPATION TIME FLUCTUATIONS OF POISSON AND EQUILIBRIUM BRANCHING SYSTEMS IN CRITICAL AND LARGE DIMENSIONS
Functional central limit theorem occupation time fluctuations branching particles systems
2009/9/18
Limit theorems are presented for the rescaled occupation
time fluctuation process of a critical finite variance branching particle system
in Rd with symmetric ®-stable motion starting off from ...