arXiv subjects

Shyan Ghosh

Publications and source records attributed to Shyan Ghosh.

4 recordsLinked to original sources

arXiv2026

Amnesic Elephant Random Walk with Polynomially Decaying Step Sizes

In this paper, we introduce an amnesic elephant random walk with polynomially decaying step sizes. The walk retains the loss of memory effect of amnesic ERW, however its step sizes decay polynomially over time. We study the effect of step-size exponent and memory parameter on the long-time behaviour of the walk. Two critical thresholds are identified that determine its phase diagram. We obtain almost sure convergence results, law of iterated logarithm, asymptotic normality and mean square displacement rate of the walk across different parameter regimes. The polynomial decay of step sizes gives rise to a subdiffusive regime while classical diffusion is recovered in the absence of decay. Also, we identify localization regimes in which the walk converges almost surely to a finite random variable.

math.PR↗

arXiv2026

On Elephant Random Walk with Delayed Amnesia

In this paper, we introduce a modified elephant random walk that exhibits a transition from a uniform memory mechanism to a selective amnesic memory mechanism. Using a vector martingale approach, we study the asymptotic behaviour of the walk across different parameter regimes. In the diffusive and critical regimes, we establish almost sure convergence results, laws of iterated logarithm, asymptotic normality of the walk, and the growth rate of mean square displacement. In the superdiffusive regime, we prove an almost sure convergence result and obtain the corresponding mean square displacement rate for the walk. Also, we study some almost sure convergence results for its center of mass. Later, we extend the model by incorporating random step sizes and obtain asymptotic results for it.

math.PR↗

arXiv2026

On multidimensional elephant random walk with stops and random step sizes

In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several convergence results for the number of moves, including the law of large numbers and the law of iterated logarithm. Using a martingale approach, we study the multidimensional elephant random walk with random step sizes. For this model, we obtain several almost sure convergence results for the number of moves, including the law of large numbers, the quadratic strong law, the law of iterated logarithm and the central limit theorem. Similar convergence results are derived for the multidimensional elephant random walk with random step sizes.

math.PR↗

arXiv2025

Multivariate Generalized Counting Process via Gamma Subordination

In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial process. We derive the explicit expressions for its joint Laplace-Stieltjes transform, its probability density function and the associated governing differential equations. Also, we study a time-changed variant of the multivariate generalized counting process where the time is changed by an independent multivariate gamma subordinator. For this time-changed process, we obtain the corresponding Lévy measure and probability mass function. Later, we discuss an application of the time-changed multivariate generalized counting process to a shock model.

math.PR↗