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Large Deviations and Quasi-Potential of a Fleming-Viot Process
Fleming-Viotprocess largedeviations quasi-potential
2009/4/29
The large deviation principle is established for the Fleming-Viot process with neutral mutation when the process starts from a point on the boundary. Since the diffusion coefficient is degenerate on t...
A Representation for Non-Colliding Random Walks
eigenvalues of random matrices Hermitian Brownian motion non-colliding Brownian motions queues in series Burke's theorem reversibility
2009/4/29
We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with respecti...
A note on r-balayages of matrix-exponential L'evy processes
L'evy process matrix-exponential distribution first exit balayage ruin theory
2009/4/29
In this note we give semi-explicit solutions for $r$-balayages of matrix-exponential-Lévy processes. To this end, we turn to an identity for the joint Laplace transform of the first entry time and the...
Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon
Gaussian random walk maximum Riemann zeta function Euler-Maclaurin summation equidistant sampling of Brownian motion finite horizon
2009/4/29
A Brownian motion observed at equidistant sampling points renders a random walk with normally distributed increments. For the difference between the expected maximum of the Brownian mo- tion and its s...
The scaling limit of senile reinforced random walk
random walk reinforcement invariance principle fractional kinetics time-change
2009/4/29
This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable cond...
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
heat equation white noise stochastic partial differential equations
2009/4/29
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
Note: Random-to-front shuffles on trees
Markov chain shuffle random-to-front random walk tree semigroup
2009/4/29
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local ``random-to-front'' reorderings, driven by a probability distribution on subsets of ...
Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
random walk in a random environment mixingmeasure
2009/4/29
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
State Tameness: A New Approach for Credit Constrains
arbitrage pricing of contingent claims continuous-time nancial markets tameness
2009/4/29
We propose a new definition for tameness within the model of security prices as Itô processes that is risk-aware. We give a new definition for arbitrage and characterize it. We then prove a t...
The Center of Mass of the ISE and the Wiener Index of Trees
ISE, Brownian snake Brownian excursion center of mass Wiener index
2009/4/28
We derive the distribution of the center of mass S of the integrated superBrownian excursion (ISE) from the asymptotic distribution of the Wiener index for simple trees. Equivalently, this is the dist...
On Long Range Percolation with Heavy Tails
Long range percolation truncation slab percolation
2009/4/28
Consider independent long range percolation on $mathbf{Z}^d$, $dgeq 2$,
where edges of length $n$ are open with
probability $p_n$. We show that if
$limsup_{ntoinfty}p_n>0,$ then there
exists an i...
We show, by a simple counterexample, that the main result in a recent paper by H. Van Zanten [Electronic Communications in Probability 7 (2002), 215-222] is false. We eventually point out the origin o...
Geometric Ergodicity and Perfect Simulation
CFTP domCFTP geometric ergodicity perfect simulation uniform ergodicity
2009/4/28
This note extends the work of Foss and Tweedie (1998), who showed that availability of the classic Coupling from the Past (CFTP) algorithm of Propp and Wilson (1996) is essentially equivalent to unifo...
Consider a two-person zero-sum game played on a random n by n matrix where the entries are iid normal random variables. Let Z be the number of rows in the support of the optimal strategy for player I ...
Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions
probabilistic Cellular Automata Interacting Particle Systems Ergodicity Gibbs measure
2009/4/28
For a general attractive Probabilistic Cellular Automata on SZ^d, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm,...