相关论文: Stochastic Master Fields

In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and temporal regularity of the generalized Ornstein-Uhlenbeck…

In this paper we construct global in time classical solutions to mean field games master equations in the lack of idiosyncratic noise in the individual agents' dynamics. These include both deterministic models and dynamics driven solely by…

The formal Heisenberg equations of the Federbush model are linearized and then are directly integrated applying the method of dynamical mappings. The fundamental role of two-dimensional free massless pseudo-scalar fields is revealed for…

A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…

In the framework of a 1D cyclic competition model, the Rock-Paper-Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled…

Complex Schroedinger equation is transformed to spinor or coupled scalar field equations replacing the imaginary unit $i$ by a matrix $\begin{bmatrix} 0 & 1 \\-1 & 0 \end{bmatrix}$. New perspecive on stochasic approach is developed with…

Master equations are of fundamental importance in modeling stochastic dynamical systems.However, solving master equations is challenging due to the exponential increase in the number of possible states or trajectories with the dimension of…

We provide a unified approach to find equilibrium solutions for time-inconsistent problems with distribution dependent rewards, which are important to the study of behavioral finance and economics. Our approach is based on {\it equilibrium…

Assuming that the mechanism proposed by Gell-Mann and Hartle works as a mechanism for decoherence and classicalization of the metric field, we formally derive the form of an effective theory for the gravitational field in a semiclassical…

We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…

We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of…

We use the truncated Wigner approximation to derive stochastic classical field equations for the description of polariton condensates. Our equations are shown to reduce to the Boltzmann equation in the limit of low polariton density. Monte…

In this paper we present a novel quasi-Newton algorithm for use in stochastic optimisation. Quasi-Newton methods have had an enormous impact on deterministic optimisation problems because they afford rapid convergence and computationally…

Inspired by recent advances in the field of expert-based approximations of Gaussian processes (GPs), we present an expert-based approach to large-scale multi-output regression using single-output GP experts. Employing a deeply structured…

We develop master equations to study perturbative stability of de Sitter Dynamical Fixed Points (DFPs) of strongly coupled massive quantum field theories in $d+1$ space-time dimensions with a holographic dual. The derived spectrum of…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…

There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical…

We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Mat\'ern class random field. The approximation method is based on the spectral compactness of the…

The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the…