This journal publishes original papers dealing with potential theory and its applications, probability theory, geometry and functional analysis and in particular estimations of the solutions of elliptic and parabolic equations; analysis of semi-groups, resolvent kernels, harmonic spaces and Dirichlet forms; Markov processes, Markov kernels, stochastic differential equations, diffusion processes and Levy processes; analysis of diffusions, heat kernels and resolvent kernels on fractals; infinite dimensional analysis, Gaussian analysis, analysis of infinite particle systems, of interacting particle systems, of Gibbs measures, of path and loop spaces; connections with global geometry, linear and non-linear analysis on Riemannian manifolds, Lie groups, graphs, and other geometric structures; non-linear or semilinear generalizations of elliptic or parabolic equations and operators; harmonic analysis, ergodic theory, dynamical systems; and boundary value problems, Martin boundaries, Poisson boundaries.

該期刊發表了關于勢理論及其應用、概率論、幾何和泛函分析，特別是橢圓方程和拋物方程解的估計的原始論文;半群、分解核、調和空間和狄利克雷形式的分析馬爾可夫過程、馬爾可夫核、隨機微分方程、擴散過程和利維過程;分形上的擴散、熱核和預分解核的分析無限維分析，高斯分析，無限粒子系統分析，相互作用粒子系統分析，吉布斯測量，路徑和回路空間分析;與全局幾何的聯系，黎曼流形、李群、圖等幾何結構的線性和非線性分析;橢圓或拋物型方程和算子的非線性或半線性推廣;諧波分析，遍歷理論，動力系統;邊值問題，馬丁邊界，泊松邊界。