The reliability of an element with alternating failure rate
The renewal theorem for random walk in two-dimensional time
The renormalization transformation for two-type branching models
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space–time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of...
The Rényi distances of Gaussian measures
The author in the paper evaluates the Rényi distances between two Gaussian measures using properties of nuclear operators and expresses the formula for the asymptotic rate of the Rényi distances of stationary Gaussian measures by the corresponding spectral density functions in a general case.
The repairman problem [Book]
The representation of Poisson functionals
The Resolvent for Simple Random Walks on the Free Product of Two Discrete Groups.
The return time theorem fails on infinite measure-preserving systems
The Reverse Isoperimetric Problem for Gaussian Measure.
The revolution of testimonies in the calculus of probabilities. (La révolution des témoignages dans le calcul des probabilités.)
The “Riemann hypothesis” for the Hawkins random Sieve
The Riesz transform for Gaussian measures
The right tail exponent of the Tracy–Widom distribution
The Tracy–Widom distribution is the large dimensional limit of the top eigenvalue of random matrix ensembles. We use the stochastic Airy operator representation to show that as the tail of the Tracy–Widom distribution satisfies
The risk-sensitive Poisson equation for a communicating Markov chain on a denumerable state space
This work concerns a discrete-time Markov chain with time-invariant transition mechanism and denumerable state space, which is endowed with a nonnegative cost function with finite support. The performance of the chain is measured by the (long-run) risk-sensitive average cost and, assuming that the state space is communicating, the existence of a solution to the risk-sensitive Poisson equation is established, a result that holds even for transient chains. Also, a sufficient criterion ensuring that...
The role of functional equations in stochastic model building.
The scaling limit of senile reinforced random walk.
The scaling limits of a heavy tailed Markov renewal process
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the -stable regenerative set. We then apply these results to the strip wetting model which is a random walk constrained above a wall and rewarded or penalized when it hits the strip where is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.
The secretary problem : optimal selection with batch-interviewing and cost
The set of probability distribution solutions of a linear functional equation
Let (Ω,,P) be a probability space and let τ: ℝ×Ω → ℝ be a function which is strictly increasing and continuous with respect to the first variable, measurable with respect to the second variable. Given the set of all continuous probability distribution solutions of the equation we determine the set of all its probability distribution solutions.
The Shannon information on a Markov chain approximately normally distributed