On the lower classes of some mixed fractional Gaussian processes with two logarithmic factors.
On the martingale problem for super-brownian motion
On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem
On the Mathematical Theory of Records
In the present work, we briefly analyze the development of the mathematical theory of records. We first consider applications associated with records. We then view distributional and limit results for record values and times. We further present methods of generation of continuous records. In the end of this work, we discuss some tests based on records.
On the Maximum of a Branching Process Conditioned on the Total Progeny
The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
On the measurement of the activity of a radioactive source and a related stochastic process.
A method is presented to compute the activity of a radioactive source. The principle of the method is based on the tuning of b, the time constant of the RC circuit of the detector with l being the rate of emission of the source, using a statistical argument.The stochastical process involved refers to the distribution of the following random voltage:Vt = ∑(0 < ti ≤ t) Yi c-b(t - ti)where the ti are Poisson dates of emission and the Yi are random or deterministic pulse heights. The case of...
On the mixed fractional Brownian motion.
On the mode-change problem for random measures.
On the moments of hitting times for random walks on trees.
On the non-equivalence of two criteria of comparability of stationary point processes
On the norms of the random walks on planar graphs
We consider the nearest neighbor random walk on planar graphs. For certain families of these graphs, we give explicit upper bounds on the norm of the random walk operator in terms of the minimal number of edges at each vertex. We show that for a wide range of planar graphs the spectral radius of the random walk is less than one.
On the Novikov-Shiryaev optimal stopping problems in continuous time.
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 occupation measure of super-Brownian motion.
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 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...