Weak Convergence of n-Particle Systems Using Bilinear Forms

Mosco Type Convergence of Bilinear Forms and Weak Convergence of n-Particle Systems

“…As an application, the particle system considered in [15] doesn't seem to be compatible with [17] or [22]. Moreover the limiting initial distribution is no longer concentrated on one single state as in [14]. However it fits the theory presented in this article.…”

“…We also want to refer to a discussion on choosing the appropriate definition of bilinear forms relative to the mathematical situation, given in [14], Subsections 2.1 and 2.3.…”

“…The convergence of the sequence Ee −βτn , n ∈ N, is then sufficient for relative compactness. This idea has been adapted to particle systems in [13] and [14] and will also be developed further in Section 3 of the present paper.…”

“…Most fundamental in this sense is [12]. In the particular case of sequences of L 2 spaces we would like to refer to [14] which has a documented history beginning 2005. Initiated by the two established generalizations of Dirichlet forms to the non-symmetric case, namely [17] and [22], also Mosco (type) convergence for non-symmetric Dirichlet forms has been investigated, cf.…”

“…[23] and [4]. The paper [14] provides a framework for nonsymmetric bilinear forms where neither the Dirichlet property nor closability is necessary. This allows to treat stochastic processes and particle systems without any connection to Dirichlet form theory.…”