15 citations · 34 across the 9 of their papers we have counts for
9 papers
Liouville distorted Brownian motion
Jiyong Shin
The Liouville Brownian motion was introduced in \cite{GRV} as a time changed process of a planar Brownian motion , where is the po…
Construction of Liouville Brownian motion via Dirichlet form theory
Jiyong Shin
The Liouville Brownian motion which was introduced in \cite{GRV} is a natural diffusion process associated with a random metric in two dimensional Liouville quantum gravity. In thi…
On singular stochastic differential equations and Dirichlet forms
Jiyong Shin, Gerald Trutnau
This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not nec…
Elliptic regularity results: n-regularized Liouville Brownian motion and non-symmetric diffusions associated with degenerate forms
Jiyong Shin
We apply improved elliptic regularity results to a concrete symmetric Dirichlet form and various non-symmetric Dirichlet forms with possibly degenerate symmetric diffusion matrix.…
Strict decomposition of diffusions associated to degenerate (sub)-elliptic forms
Jiyong Shin
For given strongly local Dirichlet forms with possibly degenerate symmetric (sub)-elliptic matrix, we show the existence of weak solutions to the stochastic differential equations…
Pointwise weak existence for diffusions associated with degenerate elliptic forms and 2-admissible weights
Jiyong Shin, Gerald Trutnau
Using analysis for 2-admissible functions in weighted Sobolev spaces and stochastic calculus for possibly degenerate symmetric elliptic forms, we construct weak solutions to a wide…
Non-symmetric distorted Brownian motion: strong solutions, strong Feller property and non-explosion results
Michael Röckner, Jiyong Shin, Gerald Trutnau
Using elliptic regularity results in weighted spaces, stochastic calculus and the theory of non-symmetric Dirichlet forms, we first show weak existence of non-symmetric distorted B…
On the stochastic regularity of distorted Brownian motions
Jiyong Shin, Gerald Trutnau
We systematically develop general tools to apply Fukushima's absolute continuity condition. These tools comprise methods to obtain a Hunt process on a locally compact separable met…
Pointwise weak existence of distorted skew Brownian motion with respect to discontinuous Muckenhoupt weights
Jiyong Shin, Gerald Trutnau
For any starting point in , we identify the stochastic differential equation that is satisfied by distorted Brownian motion with respect to a certain discontinuous Mu…