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The quadratic covariation for a weighted fractional Brownian motion
XIchao Sun, Litan Yan, Qinghua Zhang
Let be a weighted fractional Brownian motion with indices satisfying . In this paper, motivated by the asymptotic property $$ E[(B^{a,b}_{s+\va…
Quadratic covariations for the solution to a stochastic heat equation
Xichao Sun, Litan Yan, Xianye Yu
Let be the solution to a stochastic heat equation $$ \frac{\partial}{\partial t}u=\frac12\frac{\partial^2}{\partial x^2}u+\frac{\partial^2}{\partial t\partial x}X(t,x),\qu…
An integral functional driven by fractional Brownian motion
Xichao Sun, Litan Yan, Xianye Yu
Let be a fractional Brownian motion with Hurst index and the weighted local time . In this paper, we consider the integral functional $$ {\ma…
Integral with respect to the -Brownian local time
Litan Yan, Xichao Sun, Bo Gao
Let be the local time of -Brownian motion . In this paper, we prove the existence of the quadratic covariation and the integral $\int_{\mathbb R…