arXiv subjects

Sadillo Sharipov

Publications and source records attributed to Sadillo Sharipov.

5 recordsLinked to original sources

arXiv2026

Diffusion approximation of a sequence of critical branching processes with dependent immigration

This paper aims to investigate a diffusion approximation of a sequence of critical branching processes with strictly stationary and ergodic immigration. Under fairly general assumptions on the dependence structure of the immigration sequence, we establish that the scaled and properly normalized sequence of branching processes with immigration converges in distribution to the diffusion process in the Skorokhod topology. Our result extends the functional limit theorem of Wei and Winnicki (1989) to the case where the immigration sequence is dependent.

math.PR↗

arXiv2025

Strong law of large numbers for random walks in weakly dependent random scenery

In this brief note, we study the strong law of large numbers for random walks in random scenery. Under the assumptions that the random scenery is non-stationary and satisfies weakly dependent condition with an appropriate rate, we establish strong law of large numbers for random walks in random scenery. Our results extend the known results in the literature.

math.PR↗

arXiv2024

Lower deviations for branching processes with immigration

Let $\{Y_{n}$, $n \geq 1\}$ be a critical branching process with immigration having finite variance for the offspring number of particles and finite mean for the immigrating number of particles. In this paper, we study lower deviation probabilities for $Y_{n}$. More precisely, assuming that $k,n \to \infty$ such that $k=o\left(n \right)$, we investigate the asymptotics of $\mathbf{P}\left(Y_{n} \leq k \right)$ and $\mathbf{P}\left(Y_{n} = k \right)$. Our results clarify the role of the moment conditions in the local limit theorem for $Y_n$ proven by Mellein.

math.PR↗

arXiv2022

On limit theorems for functional autoregressive processes with random coefficients

In this paper, we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence, weak law of large numbers, strong law of large numbers, some exponential inequalities, central limit theorem. Our approach is based on a suitable martingale coboundary decomposition in Banach space.

math.PR↗

arXiv2022

On functional limit theorems for branching processes with dependent immigration

In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that immigration is rowwise $ψ-$mixing and the offspring mean tends to its critical value 1, immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immigration when immigration is $m-$dependent where $m$ may tend to infinity with the row index at a certain rate. In this case the limiting process is a time-changed Wiener process. Our results extend and improve the previous known results in the literature.

math.PR↗