21 citations · 64 across the 14 of their papers we have counts for
14 papers
Semi-discrete heat equations with variable coefficients and the parametrix method
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
We develop a parametrix approach for constructing solutions and establishing grid-size independent estimates for semi-discrete heat equations with variable coefficients. While the…
Convergence rate in the splitting-up method for rough differential equations
Peter H. C. Pang
In this note we construct solutions to rough differential equations with a driver , , using a…
Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
Diego Alonso-Orán, Peter H. C. Pang, Hao Tang
In this paper we investigate the effects of the interaction between time-inhomogeneous damping, non-local diffusion, and noise on classical solutions to the Camassa-Holm equation i…
Convergence of stochastic integrals with applications to transport equations and conservation laws with noise
Kenneth H. Karlsen, Peter H. C. Pang
Convergence of stochastic integrals driven by Wiener processes , with almost surely in , is crucial in analyzing SPDEs. Our focus is on the convergence of the…
The viscous variational wave equation with transport noise
Peter H. C. Pang
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove p…
Convergent finite difference schemes for stochastic transport equations
Ulrik S. Fjordholm, Kenneth H. Karlsen, Peter H. C. Pang
We present difference schemes for stochastic transport equations with low-regularity velocity fields. We establish stability and convergence of the difference approximations…
Second order commutator estimates in renormalisation theory for SPDEs with gradient-type noise
Peter H. C. Pang
An important step in standard renormalisation arguments involve convolution against a standard mollifier. As pointed out in (Punshon-Smith--Smith 2018), this generates second order…
Weak convergence of stochastic integrals
Kenneth H. Karlsen, Peter H. C. Pang
The convergence of stochastic integrals driven by a sequence of Wiener processes (with convergence in ) is crucial in the analysis of stochastic partial differentia…
Global existence of dissipative solutions to the Camassa--Holm equation with transport noise
Luca Galimberti, Helge Holden, Kenneth H. Karlsen +1
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term.…
Global well-posedness of the viscous Camassa--Holm equation with gradient noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
We analyse a nonlinear stochastic partial differential equation that corresponds to a viscous shallow water equation (of the Camassa--Holm type) perturbed by a convective, position…
Strong solutions of a stochastic differential equation with irregular random drift
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
We present a well-posedness result for strong solutions of one-dimensional stochastic differential equations (SDEs) of the form $$\mathrm{d} X= u(ω,t,X)\, \mathrm{d} t + \frac12 σ(…
The Hunter-Saxton equation with noise
Helge Holden, Kenneth H. Karlsen, Peter H. C. Pang
In this paper we develop an existence theory for the Cauchy problem to the stochastic Hunter-Saxton equatio, and prove several properties of the blow-up of its solutions. An import…
Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing
Gui-Qiang G. Chen, Peter H. C. Pang
Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and…
Nonlinear Anisotropic Degenerate Parabolic-Hyperbolic Equations with Stochastic Forcing
Gui-Qiang G. Chen, Peter H. C. Pang
We are concerned with nonlinear anisotropic degenerate parabolic-hyperbolic equations with stochastic forcing, which are heterogeneous (i.e., not space-translational invariant). A…