Variational Principle for Stochastic Processes

$(varphi_1, varphi_2)$-variational principle

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

Stochastic variational principle on riemannian manifolds

Gyarmati's Variational Principle of Dissipative Processes

Like mechanics and electrodynamics, the fundamental laws of the thermodynamics of dissipative processes can be compressed into a variational principle. This variational principle both in its differential (local) and in integral (global) forms was formulated by Gyarmati helped by the present author in 1965. This principle was applied to several fields of irreversible processes: first of all, his...

Variational Principle for

We show that some measures suuering from the so-called Renormalization Group pathologies satisfy a variational principle and that the corresponding limit of the pressure, with boundary conditions in a set of measure 1, is proportional to the pressure of the Ising model.

Gaussian Processes for Big Data through Stochastic Variational Inference

Gaussian processes [GP 10] are perhaps the dominant approach for inference on functions. They underpin a range of algorithms for regression, classification and unsupervised learning. Unfortunately, exact inference in a GP has complexity O(n) with storage demands of O(n) and this hinders application of these models for ‘big data’. Various approximate techniques have been suggested [see e.g. 1, 1...