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Since their inception about a decade ago, dynamic networks which adapt to the state of the nodes have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically…

Statistical Mechanics · Physics 2015-06-19 Kevin E. Bassler , Deepak Dhar , R. K. P. Zia

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

Machine Learning · Computer Science 2024-10-07 Yanfang Liu , Yuan Chen , Dongbin Xiu , Guannan Zhang

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…

Machine Learning · Statistics 2026-05-15 Juan-Pablo Ortega , Florian Rossmannek

The well-posedness and exponential ergodicity are proved for stochastic Hamiltonian systems containing a singular drift term which is locally integrable in the component with noise. As an application, the well-posedness and uniform…

Probability · Mathematics 2023-05-02 Panpan Ren , Martin Grothaus , Feng-Yu Wang

The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity of the associated decoupled equation and the Schauder fixed point theorem. By using Zvonkin's…

Probability · Mathematics 2021-05-14 Shao-Qin Zhang

In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…

Numerical Analysis · Mathematics 2023-01-20 Christina Schenk , David Portillo , Ignacio Romero

In this paper, we establish an existence and uniqueness result for system of quasilinear stochastic partial differential equations (SPDEs for short) with reflection in a convex domain in R^k by analytical approach. The method is based on…

Probability · Mathematics 2018-06-14 Xue Yang , Jing Zhang

We consider stochastic PDEs \[dY_t = L(Y_t)\, dt + A(Y_t).\, dB_t, t > 0\] and associated PDEs \[du_t = L u_t\, dt, t > 0\] with regular initial conditions. Here, $L$ and $A$ are certain partial differential operators involving…

Probability · Mathematics 2023-08-22 Suprio Bhar , Rajeev Bhaskaran , Arvind Kumar Nath

In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…

Statistics Theory · Mathematics 2023-06-26 Chiara Amorino , Akram Heidari , Vytautė Pilipauskaitė , Mark Podolskij

We consider a large population of learning agents noncooperatively selecting strategies from a common set, influencing the dynamics of an exogenous system (ES) we seek to stabilize at a desired equilibrium. Our approach is to design a…

Systems and Control · Electrical Eng. & Systems 2024-09-17 Jair Certório , Nuno C. Martins , Richard J. La , Murat Arcak

In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients having super-linear growth in the state variable. Second, we present…

Probability · Mathematics 2020-06-02 Chaman Kumar , Neelima , Christoph Reisinger , Wolfgang Stockinger

We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…

Probability · Mathematics 2026-04-30 Idir Arab , Milto Hadjikyriakou , Paulo Eduardo Oliveira

Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional…

Statistical Mechanics · Physics 2026-01-16 Swastik Majumder , Mustansir Barma

We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…

Populations and Evolution · Quantitative Biology 2009-11-13 Yoshimi Yoshino , Tobias Galla , Kei Tokita

In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…

Statistics Theory · Mathematics 2026-03-31 Chiara Amorino , Vytautė Pilipauskaitė

In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the…

Probability · Mathematics 2020-07-31 Zimo Hao , Michael Röckner , Xicheng Zhang

Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…

Dynamical Systems · Mathematics 2025-02-04 David Sabin-Miller , Daniel M. Abrams

We study stochastic particle systems made up of heterogeneous units. We introduce a general framework suitable to analytically study this kind of systems and apply it to two particular models of interest in economy and epidemiology. We show…

Soft Condensed Matter · Physics 2013-02-06 Luis F. Lafuerza , Raul Toral

We consider weakly interacting diffusions on the torus, for multichromatic interaction potentials. We consider interaction potentials that are not H-stable, leading to phase transitions in the mean field limit. We show that the mean field…

Mathematical Physics · Physics 2025-03-18 Benedetta Bertoli , Benjamin D. Goddard , Grigorios A. Pavliotis

Using the generalized variational framework, the strong/weak existence and uniqueness of solutions are derived for a class of distribution dependent stochastic porous media equations on general measure spaces, which also extends the…

Probability · Mathematics 2023-03-16 Jingyue Gao , Wei Hong , Wei Liu