Trifce Sandev

Macedonian Academy of Sciences and Arts

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Ralf Metzler

University of Potsdam

Ljupčo Kocarev

Macedonian Academy of Sciences and Arts

ŽT

Živorad Tomovski

University of Ostrava

Alexander Iomin

Technion – Israel Institute of Technology

E. K. Lenzi

Universidade Estadual de Maringá

Irina Petreska

Saints Cyril and Methodius University of Skopje

Aleksei V. Chechkin

Wrocław University of Science and Technology

Viktor Stojkoski

Institut Polytechnique de Bordeaux

A. Pal

Homi Bhabha National Institute

Petar Jolakoski

Macedonian Academy of Sciences and Arts

Cooperative Institutions

Saints Cyril and Methodius University of Skopje

Macedonian Academy of Sciences and Arts

Czech Academy of Sciences, Institute of Physics

University of Potsdam

University of Ss. Cyril and Methodius in Trnava

Universidade Estadual de Maringá

Universidade Estadual de Ponta Grossa

Max Planck Institute for the Physics of Complex Systems

University of Rijeka

Max Planck Society

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Cauchy Type Problems

Developments in mathematics (2019)

Trifce Sandev Živorad Tomovski

10.1007/978-3-030-29614-8_3

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Citations (4)

Fractional Schrödinger equation and anomalous relaxation: Nonlocal terms and delta potentials

Modern Physics Letters A (2021)

E. K. Lenzi L. R. Evangelista Rafael S. Zola Irina Petreska Trifce Sandev

We review and extend some results for the fractional Schrödinger equation by considering nonlocal terms or potential given in terms of delta functions. For each case, we have obtained the solution in terms of the Green function approach.

Dirac delta function

10.1142/s0217732321400046

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Citations (9)

Generalized Cattaneo (telegrapher's) equations in modeling anomalous diffusion phenomena

Physical review. E (2020)

K. Górska A. Horzela E. K. Lenzi Gianni Pagnini Trifce Sandev

We study generalized Cattaneo (telegrapher's) equations involving memory effects introduced by smearing the time derivatives. Consistency conditions where the smearing functions obey restrict freedom in their choice but the proposed scheme goes beyond the approach based on using fractional derivatives. We find conditions under which solutions of the equations considered so far can be recognized as probability distributions, i.e., are normalizable and nonnegative on their domains. Nonnegativity of solutions is demonstrated by methods of positive definite and completely monotonic functions with the Bernstein theorem being the cornerstone of the ongoing proofs. Analysis of exactly solvable examples and relevant mean-squared displacements enables us to classify diffusion processes described by such got solutions and to identify them with either ordinary or anomalous diffusion which character may change over time. To complete the present research we compare our results with those obtained using the continuous-time random-walk and the continuous-time persistent random-walk approaches.

Telegrapher's equations

10.1103/physreve.102.022128

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Citations (41)

Fractional wave equation with a frictional memory kernel of Mittag-Leffler type

Applied Mathematics and Computation (2012)

Živorad Tomovski Trifce Sandev

Kernel (algebra)

Mittag-Leffler function

10.1016/j.amc.2012.03.055

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Citations (22)

Velocity and displacement correlation functions for fractional generalized Langevin equations

Fractional Calculus and Applied Analysis (2012)

Trifce Sandev Ralf Metzler Živorad Tomovski

Mean squared displacement

Langevin equation

Anomalous Diffusion

Kernel (algebra)

Square (algebra)

10.2478/s13540-012-0031-2

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Citations (41)

Resetting dynamics in a confining potential

Journal of Physics A Mathematical and Theoretical (2020)

R. K. Singh Ralf Metzler Trifce Sandev

Abstract We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x 0 . The relaxation of this system to the steady-state exhibits a dynamic phase transition, and is achieved in a light cone region which grows linearly with time. When an absorbing boundary is introduced, effecting a symmetry breaking of the system, we find that resetting aids the barrier escape only when the particle starts on the same side as the barrier with respect to the origin. We find that the optimal resetting rate exhibits a continuous phase transition with critical exponent of unity. Exact expressions are derived for the mean escape time, the second moment, and the coefficient of variation (CV).

Constant (computer programming)

Exponent

Dynamics

Position (finance)

Reset (finance)

10.1088/1751-8121/abc83a

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Citations (40)

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

arXiv (Cornell University) (2021)

Viktor Stojkoski Petar Jolakoski A. Pal Trifce Sandev Ljupčo Kocarev

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.

Ergodicity

Position (finance)

Dynamics

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Generalised geometric Brownian motion: Theory and applications to option pricing

RePEc: Research Papers in Economics (2020)

Viktor Stojkoski Trifce Sandev Lasko Basnarkov Ljupčo Kocarev Ralf Metzler

Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for asset dynamics due to irregularities found when comparing its properties with empirical distributions. As a solution, we develop a generalisation of GBM where the introduction of a memory kernel critically determines the behavior of the stochastic process. We find the general expressions for the moments, log-moments, and the expectation of the periodic log returns, and obtain the corresponding probability density functions by using the subordination approach. Particularly, we consider subdiffusive GBM (sGBM), tempered sGBM, a mix of GBM and sGBM, and a mix of sGBMs. We utilise the resulting generalised GBM (gGBM) to examine the empirical performance of a selected group of kernels in the pricing of European call options. Our results indicate that the performance of a kernel ultimately depends on the maturity of the option and its moneyness.

Kernel (algebra)

Stochastic discount factor

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Harmonic and anharmonic quantum-mechanical oscillators in noninteger dimensions

Physics Letters A (2013)

Trifce Sandev Irina Petreska E. K. Lenzi

Laguerre polynomials

Legendre transformation

Resummation

10.1016/j.physleta.2013.10.048

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Citations (29)

Solutions to the Schrödinger Equation: Nonlocal Terms and Geometric Constraints

Mathematics (2025)

Irina Petreska Pece Trajanovski Trifce Sandev Jonathan A. M. Almeida Rocha A. S. M. de Castro

Here, we investigate a three-dimensional Schrödinger equation that generalizes the standard framework by incorporating geometric constraints. Specifically, the equation is adapted to account for a backbone structure exhibiting memory effects dependent on both time and spatial position. For this, we incorporate an additional term in the Schrödinger equation with a nonlocal dependence governed by short- or long-tailed distributions characterized by power laws associated with Lévy distributions. This modification also introduces a backbone structure within the system. We derive solutions that reveal various behaviors using Green’s function approach expressed in terms of Fox H-functions.

10.3390/math13010137

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