Variational principle for stochastic singular control of mean-field Lévy-forward-backward system driven by orthogonal Teugels martingales with application

2017 ◽  
Vol 28 (2) ◽  
pp. 97 ◽  
Author(s):  
Mokhtar Hafayed ◽  
Shahlar Meherrem ◽  
Deniz H. Gucoglu ◽  
Saban Eren
Keyword(s):  
Variational Principle ◽  
Mean Field ◽  
Singular Control ◽  
Teugels Martingales

The unbounded two-dimensional guiding-centre plasma

1995 ◽  
Vol 54 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Michael K. -H. Kiessling
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Mean Field ◽  
Analytical Techniques ◽  
Larmor Frequency ◽  
Two Dimensional ◽  
Algebraic Relation ◽  
Density Profiles ◽  
Translation Invariant ◽  
Computer Based

The thermal mean-field equilibrium of a translation-invariant, unbounded one- component guiding-centre plasma is studied by analytical techniques. A variational principle is constructed. It is shown that only radial symmetric, decreasing density profiles occur. Prescribing the total number of gyro centres N ∈ (0, ∞), the energy E ∈ (E0, ∞) and the canonical angular momentum M ∈ (0, ∞]) uniquely determines a profile. Metastable or unstable profiles do not exist. A simple algebraic relation between N, M, the guiding-centre temperature β−1 and the characteristic Larmor frequency ω is derived. This explains Williamson's computer-based observations.

scholarly journals THE EXTENDED VARIATIONAL PRINCIPLE FOR MEAN-FIELD, CLASSICAL SPIN SYSTEMS

2005 ◽  
Vol 17 (10) ◽  
pp. 1209-1239
Author(s):  
E. KRITCHEVSKI ◽  
S. STARR
Keyword(s):  
Variational Principle ◽  
Optimization Problems ◽  
Mean Field ◽  
Spin Systems ◽  
Field Equations ◽  
Convex Optimization Problems ◽  
Mean Field Equations ◽  
Statistical Mechanical ◽  
Thermodynamic Pressure ◽  
Extended Variational Principle

The purpose of this article is to obtain a better understanding of the extended variational principle (EVP). The EVP is a formula for the thermodynamic pressure of a statistical mechanical system as a limit of a sequence of minimization problems. It was developed for disordered mean-field spin systems, spin systems where the underlying Hamiltonian is itself random, and whose distribution is permutation invariant. We present the EVP in the simpler setting of classical mean-field spin systems, where the Hamiltonian is non-random and symmetric. The EVP essentially solves these models. We compare the EVP with another method for mean-field spin systems: the self-consistent mean-field equations. The two approaches lead to dual convex optimization problems. This is a new connection, and it permits a generalization of the EVP.

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