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On \(L^p\) Liouville Theorems for Dirichlet Forms
We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima’s ergodic theorem for the harmonic functions in...
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The Probabilistic Solution of a System of Semilinear Elliptic PDEs Under the Third Boundary Conditions
In this paper, we establish existence and uniqueness of weak (Sobolev) solution to the third boundary value problem for a class of semilinear...
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Stochastic Processes in the Decades after 1950
Paul-André Meyer (1934–2003), founder and leader of the Strasbourg school of probability, worked from the 1960s into the 1990s on the theory of...
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Inexact proximal DC Newton-type method for nonconvex composite functions
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly...
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Skeleton Decomposition and Law of Large Numbers for Supercritical Superprocesses
The goal of this paper is twofold. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general...
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A smoothing quasi-Newton method for solving general second-order cone complementarity problems
Recently, there are much interests in studying smoothing Newton method for solving montone second-order cone complementarity problem (SOCCP) or...
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Backward Stochastic Differential Equations and Dirichlet Problems of Semilinear Elliptic Operators with Singular Coefficients
In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order...
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The α-orthogonal complements of regular Dirichlet subspaces for one-dimensional Brownian motion
Roughly speaking a regular Dirichlet subspace of a Dirichlet form is a subspace which is also a regular Dirichlet form on the same state space. In...
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General analytic characterization of gaugeability for Feynman-Kac functionals
We give a general analytic characterization of the gaugeability for generalized Feynman-Kac functionals involving continous additive functionals...
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Law of Large Numbers for Branching Symmetric Hunt Processes with Measure-Valued Branching Rates
We establish weak and strong laws of large numbers for a class of branching symmetric Hunt processes with the branching rate being a smooth measure...
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Bivariate Revuz Measures and the Feynman-Kac Formula on Semi-Dirichlet Forms
In this paper we shall first establish the theory of bivariate Revuz correspondence of positive additive functionals under a semi-Dirichlet form...
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Spherical decomposition of electromagnetic fields generated by quasi-static currents
The spherical decomposition of electromagnetic fields generated by an arbitrary distribution of quasi-static currents may be obtained from the...
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Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms
Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the...
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Martingale Representations for Diffusion Processes and Backward Stochastic Differential Equations
In this paper we explain that the natural filtration of a continuous Hunt process is continuous, and show that martingales over such a filtration are...
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Explosion of Jump-Type Symmetric Dirichlet Forms on ℝ d
We give a sufficient condition for a class of jump-type symmetric Dirichlet forms on ℝ d to be conservative in terms of the jump kernel and the...