3 citations · 4 across the 9 of their papers we have counts for
9 papers
A Feynman-Kac approach for the spatial derivative of the solution to the Wick stochastic heat equation driven by time homogeneous white noise
Hyun-Jung Kim, Ramiro Scorolli
We consider the (unique) mild solution of a 1-dimensional stochastic heat equation on driven by time-homogeneous white noise in the Wick-Skorokhod s…
Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach
Igor Cialenco, Hyun-Jung Kim, Gregor Pasemann
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic proce…
Parameter estimation for discretely sampled stochastic heat equation driven by space-only noise
Igor Cialenco, Hyun-Jung Kim
We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when…
Drift Estimation for Discretely Sampled SPDEs
Igor Cialenco, Francisco Delgado-Vences, Hyun-Jung Kim
The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an…
Statistical Analysis of Some Evolution Equations Driven by Space-only Noise
Igor Cialenco, Hyun-Jung Kim, Sergey V. Lototsky
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniq…
An Asymptotic Comparison of Two Time-homogeneous PAM Models
Hyun-Jung Kim, Sergey V. Lototsky
Both Wick-Ito-Skorokhod and Stratonovich interpretations of the parabolic Anderson model (PAM) lead to solutions that are real analytic as functions of the noise intensity e, and,…
Stochastic parabolic Anderson model with time-homogeneous generalized potential: Mild formulation of solution
Hyun-Jung Kim
A mild formulation for stochastic parabolic Anderson model with time-homogeneous Gaussian potential suggests a way of defining a solution to obtain its optimal regularity. Two diff…
Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution
H. -J. Kim, S. V. Lototsky
A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a Hölder continuous funct…
Time-Homogeneous Parabolic Wick-Anderson Model in One Space Dimension: Regularity of Solution
Hyun-Jung Kim, Sergey V Lototsky
Even though the heat equation with random potential is a well-studied object, the particular case of time-independent Gaussian white noise in one space dimension has yet to receive…