Yukawa Potential, Panharmonic Measure and Brownian Motion

Classical Potential Theory and Brownian Motion

Pioneering work of Doob, Kac, and Kakutani showed that there was a beautiful and deep connection between certain problems in the study of Brownian motion and those of classical potential theory. This work stimulated much research on the theory of Markov processes. In spite of all this work, however, there doesn't appear anywhere in the literature any reasonably complete treatment of the connect...

Brownian Motion: The Link Between Probability and Mathematical Analysis

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Potential Theory of Subordinate Brownian Motion

G–Brownian Motion and Dynamic Risk Measure under Volatility Uncertainty

Packing Measure of the Sample Paths of Fractional Brownian Motion

Let X(t) (t ∈ R) be a fractional Brownian motion of index α in Rd. If 1 < αd , then there exists a positive finite constant K such that with probability 1, φ-p(X([0, t])) = Kt for any t > 0 , where φ(s) = s 1 α /(log log 1 s ) 1 2α and φ-p(X([0, t])) is the φ-packing measure of X([0, t]).