Consider the heat equation: \begin{equation}\label{eq:00} \begin{cases} \displaystyle du(t,x)=\frac12\Delta u(t,x)\,dt+b(u(t,x))\,dt,&t>0,\ x\in D,\\[1mm] u(t,x)=0,&t\ge0,\ x\in\partial D, u(0,x)=u_0(x),&x\in D. \end{cases} \end{equation} It is well known that superlinear growth of the coefficient $b$ may lead to finit...
We establish the Varadhan small-time asymptotics for the quenched and annealed heat kernels of one-dimensional diffusions in a random environment with generator $\mathcal L_W f(x)=e^{-\rho(x,W)}(e^{a(x,W)}f'(x))'$. The coefficients $a$ and $\rho$ are continuous in space and satisfy a local exponential moment condition....
In this paper, we establish a small-time annealed path large deviation principle for one-dimensional diffusions in a random environment associated with the generator ${\mathcal L}_W f(x)=e^{-\rho(x,W)}(e^{a(x,W)}f'(x))'$. The coefficients $\{\rho(x,\cdot):x\in\mathbb R\}$ and $\{a(x,\cdot):x\in\mathbb R\}$ are random....
In this paper, we establish a small-time annealed path large deviation principle for one-dimensional diffusions in a random environment associated with the generator ${\mathcal L}_W f(x)=e^{-\rho(x,W)}(e^{a(x,W)}f'(x))'$. The coefficients $\{\rho(x,\cdot):x\in\mathbb R\}$ and $\{a(x,\cdot):x\in\mathbb R\}$ are random....
We establish the well-posedness of stochastic scalar conservation laws on moving hypersurfaces driven by Brownian motion. To handle the interaction between stochastic forcing and evolving geometry, we derive an It\^{o} formula on moving surfaces and introduce the notion of generalized entropy solutions incorporating th...
Ping Chen, Tu-Sheng Zhang· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
