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Related papers: Mean-field stochastic Volterra equations

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This paper provides a Feller's test for explosions of one-dimensional continuous stochastic Volterra processes of convolution type. The study focuses on dynamics governed by nonsingular kernels, which preserve the semimartingale property of…

Probability · Mathematics 2024-06-21 Alessandro Bondi , Sergio Pulido

We propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain…

Probability · Mathematics 2019-07-18 Nils Detering , Jean-Pierre Fouque , Tomoyuki Ichiba

This paper investigates the well-posedness of singular mean-field backward stochastic Volterra integral equations (MF-BSVIEs) in infinite-dimensional spaces. We consider the equation: \[X(t) = \Psi(t) + \int_t^b P\big(t, s, X(s), \aleph(t,…

Probability · Mathematics 2024-12-10 Javad A. Asadzade , Nazim I. Mahmudov

Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic…

Mathematical Physics · Physics 2012-04-26 Denis Sidorov

Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…

Probability · Mathematics 2025-03-04 Pierre Monmarché

This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…

Classical Analysis and ODEs · Mathematics 2011-03-01 Basak Karpuz

This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…

Analysis of PDEs · Mathematics 2021-08-26 Noufel Frikha , Paul-Eric Chaudru de Raynal

Mean-field backward stochastic Volterra integral equations (MF-BSVIEs, for short) are introduced and studied. Well-posedness of MF-BSVIEs in the sense of introduced adapted M-solutions is established. Two duality principles between linear…

Probability · Mathematics 2011-07-06 Yufeng Shi , Tianxiao Wang , Jiongmin Yong

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

Probability · Mathematics 2026-04-28 Martin Bergerhausen , David J. Prömel

We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite dimensional system of standard backward SDEs and establish its well-posedness, and we show…

Probability · Mathematics 2020-08-05 Camilo Hernández , Dylan Possamaï

This paper provide a comprehensive analysis of the finite and long time behavior of continuous-time non-Markovian dynamical systems, with a focus on the forward Stochastic Volterra Integral Equations(SVIEs).We investigate the properties of…

Probability · Mathematics 2025-11-06 Emmanuel Gnabeyeu , Gilles Pagès

This paper investigates the limit distribution of discretization errors in stochastic Volterra equations (SVEs) with general multidimensional kernel structures. While prior studies, such as Fukasawa and Ugai (2023), were focused on…

Probability · Mathematics 2025-04-08 Masaaki Fukasawa , Minato Hojo

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear…

Probability · Mathematics 2008-12-05 Xicheng Zhang

In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper…

Probability · Mathematics 2007-05-23 Anna Karczewska

Volterra observations systems with scalar kernels are studied. New sufficient conditions for admissibility of observation operators are developed. The obtained results are applied to time-fractional diffusion equations of distributed order.

Analysis of PDEs · Mathematics 2009-07-10 Bernhard Hermann Haak , Birgit Jacob

We consider a general McKean-Vlasov stochastic differential equation driven by a rotationally invariant $\alpha$-stable process on $\mathbb{R}^d$ with $\alpha \in (1,2)$. We assume that the diffusion coefficient is the identity matrix and…

Analysis of PDEs · Mathematics 2024-01-29 Thomas Cavallazzi

We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To…

Probability · Mathematics 2025-03-28 Jani Nykänen

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

Probability · Mathematics 2025-01-07 Lei Li , Yuelin Wang , Yuliang Wang

In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of…

Numerical Analysis · Mathematics 2023-04-25 Ilya Boykov , Vladimir Roudnev , Alla Boykova

We consider particle systems that evolve by inertialess binary interaction through general non-attractive kernels of singularity $|x|^{-\alpha}$ with $\alpha<d-1$. We prove a quantitative mean-field limit in terms of Wasserstein distances…

Analysis of PDEs · Mathematics 2025-09-18 Richard M. Höfer , Richard Schubert