arXiv subjects

Verdiana Mustaro

Publications and source records attributed to Verdiana Mustaro.

3 recordsLinked to original sources

arXiv2026

On Analytically Tractable Multidimensional Diffusions via Doob h-Transforms, with Resetting and Applications to Wiener and Ornstein--Uhlenbeck Processes

We investigate a class of drift transformations of multidimensional diffusion processes generated through Doob $h$-transforms. These transformations provide a systematic approach for constructing analytically tractable stochastic models with prescribed probabilistic and statistical properties. We derive sufficient conditions under which the transformed diffusion admits an explicit transition density expressed through a product form involving a strictly positive harmonic function. Particular choices of this function lead to mixture representations of the transition density and to bimodality. We further analyze the effects of the transformation on stochastic ordering, diffusions in potential landscapes, and Poissonian resetting dynamics. In particular, we show that the product-form relation is preserved under resetting, enabling explicit characterization of the corresponding stationary distributions. Two multidimensional examples based on Wiener and Ornstein--Uhlenbeck processes illustrate the theory, providing closed-form expressions for transition densities, weight functions, and effective potentials. The two-dimensional setting is explored in detail, including symmetry effects and absorbing boundaries.

math.PR↗

arXiv2026

Strategic Partitioning and Manipulability in Two-Round Elections

We consider a two-round election model involving $m$ voters and $n$ candidates. Each voter is endowed with a strict preference list ranking the candidates. In the first round, the candidates are partitioned into two subsets, $A$ and $B$, and voters select their preferred candidate from each. Provided there are no ties, the two respective winners advance to a second round, where voters choose between them according to their initial preference lists. We analyze this scenario using a probabilistic framework based on a spatial voting model with cyclically constructed preference lists and uniformly distributed ideal points. Our objective is to determine the optimal initial partition of $A$ and $B$ that maximizes a target candidate's probability of winning. We analytically evaluate this success probability and derive its asymptotic behavior as the number of candidates $n \to \infty$. A key finding is that the asymptotically optimal relative width of the main discrete cluster converges precisely to one-fifth of the total number of candidates. Finally, we provide computational results and confidence intervals derived from simulation algorithms that validate the analytical framework. Specifically, we demonstrate that the probability of the universal victory event rapidly approaches $1$ as the electorate size increases.

cs.GT↗

arXiv2023

On the telegraph process driven by geometric counting process with Poisson-based resetting

We investigate the effects of the resetting mechanism to the origin for a random motion on the real line characterized by two alternating velocities $v_1$ and $v_2$. We assume that the sequences of random times concerning the motions along each velocity follow two independent geometric counting processes of intensity $λ$, and that the resetting times are Poissonian with rate $ξ>0$. Under these assumptions we obtain the probability laws of the modified telegraph process describing the position and the velocity of the running particle. Our approach is based on the Markov property of the resetting times and on the knowledge of the distribution of the intertimes between consecutive velocity changes. We obtain also the asymptotic distribution of the particle position when (i) $λ$ tends to infinity, and (ii) the time goes to infinity. In the latter case the asymptotic distribution arises properly as an effect of the resetting mechanism. A quite different behavior is observed in the two cases when $v_2<0<v_1$ and $0<v_2<v_1$. Furthermore, we focus on the determination of the moment-generating function and on the main moments of the process describing the particle position under reset. Finally, we analyse the mean-square distance between the process subject to resets and the same process in absence of resets. Quite surprisingly, the lowest mean-square distance can be found for $ξ=0$, for a positive $ξ$, or for $ξ\to +\infty$ depending on the choice of the other parameters.

math.PR↗