Limit theorems and variation properties for fractional derivatives of the local time of a stable process
Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions.
Limit theorems for discrete-time metapopulation models.
Limit theorems for exceedances of sequence of branching processes.
Limit Theorems for Non-Critical Branching Processes with Continuous State Space
2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.In the paper a modification of the branching stochastic process with immigration and with continuous states introduced by Adke S. R. and Gadag V. G. (1995) is considered. Limit theorems for the non-critical processes with or without non-stationary immigration and finite variance are proved. The subcritical case is illustrated with examples.
Limit theorems for number of diffusion processes, which did not absorb by boundaries
We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.
Limit theorems for one-dimensional transient random walks in Markov environments
Limit theorems for Parrondo's paradox.
Limit Theorems for Regenerative Excursion Processes
This work is supported by Bulgarian NFSI, grant No. MM–704/97The regenerative excursion process Z(t), t = 0, 1, 2, . . . is constructed by two independent sequences X = {Xi , i ≥ 1} and Z = {Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}. For the embedded alternating renewal process, with interarrival times Xi – the time for the installation and Ti – the time for the work, are proved some limit theorems for the spent worktime and the residual worktime, when at least one of the means of Xi and Ti is infinite. ...
Limit theorems for some functionals with heavy tails of a discrete time Markov chain
Consider an irreducible, aperiodic and positive recurrent discrete time Markov chain (Xn,n ≥ 0) with invariant distribution μ. We shall investigate the long time behaviour of some functionals of the chain, in particular the additive functional S n = ∑ i = 1 n f ( X i ) for a possibly non square integrable functionf. To this end we shall link ergodic properties of the chain to mixing properties, extending known results in the continuous time case. We will then use existing results of convergence...
Limit theorems for stationary Markov processes with L2-spectral gap
Let be a discrete or continuous-time Markov process with state space where is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. is assumed to be a Markov additive process. In particular, this implies that the first component is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process is shown to satisfy the...
Limit theorems for stochastic recursions with Markov dependent coefficients
We consider the stochastic recursion for Markov dependent coefficients (Aₙ,Bₙ) ∈ ℝ⁺ × ℝ. We prove the central limit theorem, the local limit theorem and the renewal theorem for the partial sums Sₙ = X₁+ ⋯ + Xₙ.
Limit theorems for subcritical branching processes in random environment
Limit theorems for the process of exceedances in large populations.
Limit theorems in the boundary hitting problem for a multidimensional random walk.
Limit velocity for a driven particle in a random medium with mass aggregation
Limite ergodique de processus de diffusion infini-dimensionnels.
We give a temporal ergodicity criterium for the solution of a class of infinite dimensional stochastic differential equations of gradient type, where the interaction has infinite range. We illustrate our theoretical result by typical examples.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
Limites non tangentielles, limites browniennes en probabilité et limites semi-fines.
Limiting angle of brownian motion in certain two-dimensional Cartan-Hadamard manifolds