On the number of local extrema in a sequence of independent random variables
On the number of representations of an element in a polygonal Cayley graph
We compute explicitly the number of paths of given length joining two vertices of the Cayley graph of the free product of cyclic groups of order k.
On the number of word occurrences in a semi-Markov sequence of letters
Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.
On the occupation measure of super-Brownian motion.
On the occupation time of Brownian excursion.
On the Onsager-Machlup functional for elliptic diffusion processes
On the optimal strategy in a random game.
On the order of growth of convergent series of independent random variables.
On the Oscillation Functions of Gaussian Processes.
On the parabolic generator of a general one-dimensional Lev́y process.
On the paradox of n random variables
On the partial sums of Walsh-Fourier series
We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.
On the path structure of a semimartingale arising from monotone probability theory
Let X be the unique normal martingale such that X0=0 and d[X]t=(1−t−Xt−) dXt+dt and let Yt:=Xt+t for all t≥0; the semimartingale Y arises in quantum probability, where it is the monotone-independent analogue of the Poisson process. The trajectories of Y are examined and various probabilistic properties are derived; in particular, the level set {t≥0: Yt=1} is shown to be non-empty, compact, perfect and of zero Lebesgue measure. The local times of Y are found to be trivial except for that at level...
On the pathwise uniqueness of solutions of stochastic differential equations.
On the persistence of decorrelation in the theory of wave turbulence
We study the statistical properties of the solutions of the Kadomstev-Petviashvili equations (KP-I and KP-II) on the torus when the initial datum is a random variable. We give ourselves a random variable with values in the Sobolev space with big enough such that its Fourier coefficients are independent from each other. We assume that the laws of these Fourier coefficients are invariant under multiplication by for all . We investigate about the persistence of the decorrelation between the...
On the perturbation of Markov chains with nearly transient states.
On the Poisson approximation of the binomial distribution.
On the Poisson approximation to the negative hypergeometric distribution.
On the Poisson equation in the potential theory of a single kernel.
On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations.