4 papers
A submartingale for the probability of avoiding the origin in one-point interaction ground-state diffusion:
Barkat Mian
We study the near-origin behavior on of the singular diffusion whose transition density is given by a Doob transform of the integral kernel of the semigroup generated by th…
Pathwise structure of the three-dimensional attractive one-point interaction diffusion
Barkat Mian
We study the pathwise behavior of the three-dimensional attractive one-point interaction diffusion whose law was constructed by Cranston, Koralov, Molchanov and Vainberg, correspon…
A dyadic construction of a three-dimensional attractive point interaction Markov family
Barkat Mian
We discuss a probabilistic approximation framework for the three-dimensional attractive point interaction on a finite time horizon. By iterating the Doob transforms of the explicit…
Planar diffusions with a point interaction on a finite time horizon
Barkat Mian
The skew-product diffusion [Ann. Appl. Probab. 35, 3150--3214 (2025)] and exponentially tilted planar Brownian motion [Electron. J. Probab. 30, 1--97 (2025)] are canonical examples…