arXiv subjects

Petar Jolakoski

Publications and source records attributed to Petar Jolakoski.

11 recordsLinked to original sources

arXiv2026

Ridge Regression from Poisson Resetting: A Renewal Perspective on Spectral Regularization

We connect stochastic resetting from non-equilibrium statistical physics with ridge regularization in statistical learning. For linear gradient flow, resetting to the origin at rate $r$ produces stationary mean $(X^\top X+rI)^{-1}X^\top y$, exactly the ridge estimator with penalty $λ=r$. This uses the known Laplace-transform relationship between ridge regression and exponential-time averaging of gradient flow, with the exponential time now interpreted as the stationary age associated with Poisson resetting. We then extend this identity to general renewal reset laws: the exponential reset time distribution is the unique renewal law whose stationary mean reproduces scalar ridge in every eigendirection as an exact filter identity for every positive curvature, while non-exponential renewal laws generate alternative spectral filters. At the fluctuation level, we study a separate additive Ornstein-Uhlenbeck extension with constant diffusion, interpreted as a stylized SGD approximation. In this setting, the equality holds only at the level of the mean, since the reset process has a nonzero stationary covariance from accumulated OU noise and reset-timing variance, whereas deterministic ridge is a fixed estimator with the same center. Stylized experiments compare the deterministic renewal-induced filters directly and illustrate when filters induced by non-exponential reset-time laws can differ predictively from ridge. The results for the stationary mean and the induced spectral filters are established for continuous-time gradient flow with isotropic resetting on quadratic objectives; the covariance and risk formulas additionally assume additive noise with state-independent covariance.

cs.LG↗

arXiv2026

Business cycle synchronization between the EU and Western Balkan candidate economies: A Wavelet Analysis

Business cycle synchronization between EU and Western Balkan candidate economies is usually modeled with aggregate time-domain correlations that mix short-run and long-run dynamics. This paper addresses that limitation by combining wavelet-based time-frequency decomposition with Bayesian zero-inflated beta regression. Using annual dyad-year data for 2001--2021, we estimate synchronization separately at shorter (1.5--4.5 years) and longer (4.5--8.5 years) horizons and relate each horizon to its correlates. The results show that EU--WB dyads are less synchronized than EU--EU dyads in the short run, and that trade deepening over time is more positively associated with short-run synchronization in EU--WB pairs. At longer horizons, the positive association between shared EU/EMU membership and synchronization weakens or reverses when the same country pair moves into deeper institutional integration, while differences across country pairs in average EU/EMU status become negligible. Over the same horizon, trade deepening within a pair is more consistently associated with synchronization, and more persistent structural dissimilarity is associated with lower synchronization. EU--WB dyads are no longer clearly less synchronized at these frequencies, and the remaining convergence pattern is more consistent with sectoral differences narrowing over time than with trade. These findings indicate that synchronization channels are horizon-dependent and that conclusions based on single-horizon correlation measures can obscure the distinction between short-term coupling and structural convergence.

econ.GN↗

arXiv2025

Response to an external field of a generalized Langevin equation with stochastic resetting of the memory kernel

We study a generalized Langevin equation (GLE) framework that incorporates stochastic resetting of a truncation power-law memory kernel. The inclusion of stochastic resetting enables the emergence of resonance phenomena even in parameter regimes where conventional settings (without resetting) do not exhibit such behavior. Specifically, we explore the response of the system to an external field under three scenarios: (i) a free particle, (ii) a particle in a harmonic potential, and (iii) the effect of truncation in the memory kernel. In each case, the primary focus is on understanding how the resetting mechanism interacts with standard parameters to induce stochastic resonance. In addition, we explore the effect of resetting on the dielectric loss.

cond-mat.stat-mech↗

arXiv2024

The impact of stochastic resetting on resource allocation: The case of Reallocating geometric Brownian motion

We study the effects of stochastic resetting on the Reallocating geometric Brownian motion (RGBM), an established model for resource redistribution relevant to systems such as population dynamics, evolutionary processes, economic activity, and even cosmology. The RGBM model is inherently non-stationary and non-ergodic, leading to complex resource redistribution dynamics. By introducing stochastic resetting, which periodically returns the system to a predetermined state, we examine how this mechanism modifies RGBM behavior. Our analysis uncovers distinct long-term regimes determined by the interplay between the resetting rate, the strength of resource redistribution, and standard geometric Brownian motion parameters: the drift and the noise amplitude. Notably, we identify a critical resetting rate beyond which the self-averaging time becomes effectively infinite. In this regime, the first two moments are stationary, indicating a stabilized distribution of an initially unstable, mean-repulsive process. We demonstrate that optimal resetting can effectively balance growth and redistribution, reducing inequality in the resource distribution. These findings help us understand better the management of resource dynamics in uncertain environments.

cond-mat.stat-mech↗

arXiv2023

Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It also tends to a drift towards its mean function, and such a process is called mean-reverting. Two examples of the generalized Ornstein-Uhlenbeck process are considered. In the first one, we study the Ornstein-Uhlenbeck process on a comb model, as an example of the harmonically bounded random motion in the topologically constrained geometry. The main dynamical characteristics (as the first and the second moments) and the probability density function are studied in the framework of both the Langevin stochastic equation and the Fokker-Planck equation. The second example is devoted to the study of the effects of stochastic resetting on the Ornstein-Uhlenbeck process, including stochastic resetting in the comb geometry. Here, the non-equilibrium stationary state is the main question in task, where the two divergent forces, namely the resetting and the drift towards the mean, lead to compelling results both in the case of the Ornstein-Uhlenbeck process with resetting and its generalization on the two dimensional comb structure.

cond-mat.stat-mech↗

arXiv2022

The fate of the American dream: A first passage under resetting approach to income dynamics

Detailed knowledge of individual income dynamics is crucial for investigating the existence of the American dream: Are we able to improve our income status during our working life? This key question simply boils down to observing individual status and how it moves between two thresholds: the current income and the desired income. Yet, our knowledge of these temporal properties of income remains limited since we rely on estimates coming from transition matrices which simplify income dynamics by aggregating the individual changes into quantiles and thus overlooking significant microscopic variations. Here, we bridge this gap by employing First Passage Time concepts in a baseline stochastic process with resetting used for modeling income dynamics and developing a framework that is able to crucially disaggregate the temporal properties of income to the level of an individual worker. We find analytically and illustrate numerically that our framework is orthogonal to the transition matrix approach and leads to improved and more granular estimates. Moreover, to facilitate empirical applications of the framework, we introduce a publicly available statistical methodology, and showcase the application using the USA income dynamics data. These results help to improve our understanding on the temporal properties of income in real economies and provide a set of tools for designing policy interventions.

econ.GN↗

arXiv2022

Correlates of the country differences in the infection and mortality rates during the first wave of the COVID-19 pandemic: Evidence from Bayesian model averaging

In the initial wave of the COVID-19 pandemic we observed great discrepancies in both infection and mortality rates between countries. Besides the biological and epidemiological factors, a multitude of social and economic criteria also influence the extent to which these discrepancies appear. Consequently, there is an active debate regarding the critical socio-economic and health factors that correlate with the infection and mortality rates outcome of the pandemic. Here, we leverage Bayesian model averaging techniques and country level data to investigate the potential of 28 variables, describing a diverse set of health and socio-economic characteristics, in being correlates of the final number of infections and deaths during the first wave of the coronavirus pandemic. We show that only few variables are able to robustly correlate with these outcomes. To understand the relationship between the potential correlates in explaining the infection and death rates, we create a Jointness Space. Using this space, we conclude that the extent to which each variable is able to provide a credible explanation for the COVID-19 infections/mortality outcome varies between countries because of their heterogeneous features.

physics.soc-ph↗

arXiv2021

Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity

We explore the role of non-ergodicity in the relationship between income inequality, the extent of concentration in the income distribution, and mobility, the feasibility of an individual to change their position in the income distribution. For this purpose, we explore the properties of an established model for income growth that includes "resetting" as a stabilising force which ensures stationary dynamics. We find that the dynamics of inequality is regime-dependent and may range from a strictly non-ergodic state where this phenomenon has an increasing trend, up to a stable regime where inequality is steady and the system efficiently mimics ergodic behaviour. Mobility measures, conversely, are always stable over time, but the stationary value is dependent on the regime, suggesting that economies become less mobile in non-ergodic regimes. By fitting the model to empirical data for the dynamics of income share of the top earners in the United States, we provide evidence that the income dynamics in this country is consistently in a regime in which non-ergodicity characterises inequality and immobility dynamics. Our results can serve as a simple rationale for the observed real world income dynamics and as such aid in addressing non-ergodicity in various empirical settings across the globe.

econ.GN↗

arXiv2021

Determinants of budget deficits: Focus on the effects from the COVID-19 crisis

This paper revisits the discussion on determinants of budget balances and investigates the change in their effect in light of the COVID-19 crisis by utilizing data on 43 countries and a system generalized method of moments approach. The results show that the overall impact of the global pandemic led to a disproportionate increase in the magnitude of the estimated effects of the macroeconomic determinants on the budget balance. However, we also find that more developed economies were able to undertake higher stimulus packages for the relatively same level of primary balance. We believe that one of the factors affecting this outcome is that that they exhibit a higher government debt position in domestic currency denomination.

econ.GN↗

arXiv2021

The impact of state capacity on the cross-country variations in COVID-19 vaccination rates

The initial period of vaccination shows strong heterogeneity between countries' vaccinations rollout, both in the terms of the start of the vaccination process and in the dynamics of the number of people that are vaccinated. A predominant thesis in the ongoing debate on the drivers of this observed heterogeneity is that a key determinant of the swift and extensive vaccine rollout is state capacity. Here, we utilize two measures that quantify different aspects of the state capacity: i) the external capacity (measured through the soft power and the economic power of the country) and ii) the internal capacity (measured via the country's government effectiveness) and investigate their relationship with the coronavirus vaccination outcome in the initial period (up to 30th January 2021). By using data on 189 countries and a two-step Heckman approach, we find that the economic power of the country and its soft power are robust determinants of whether a country has started with the vaccination process. In addition, the government effectiveness is a key factor that determines vaccine roll-out. Altogether, our findings are in line with the hypothesis that state capacity determines the observed heterogeneity between countries in the initial period of COVID-19 vaccines rollout.

econ.GN↗

arXiv2020

The short-run impact of COVID-19 on the activity in the insurance industry in the Republic of North Macedonia

This paper investigates the impact of the COVID-19 pandemic on the insurance industry in the Republic of North Macedonia during the first half of 2020. By utilizing seasonal autoregressive models and data for 11 insurance classes, we find that the insurance activity shrank by more than 10% compared to what was expected. The total loss in the industry was, however, much less than the amount of funds made available by the Insurance Supervision Agency. This was because the pandemic induced changes in the activity structure - the share of Motor vehicles class fell at the expense of the property classes.

q-fin.RM↗