Strong Solutions and Strong Feller Properties for Regime-Switching Diffusion Processes in An Infinite State Space

Regime-switching diffusion processes: strong solutions and strong Feller property

We investigate the existence and uniqueness of strong solutions up to an explosion time for regime-switching diffusion processes in an infinite state space. Instead of concrete conditions on coefficients, our existence and uniqueness result is established under the general assumption that the diffusion in every fixed environment has a unique non-explosive strong solution. Moreover, non-explosio...

Strong Solutions for Pair Diffusion Models in Homogeneous Semiconductors

Insulating state of granular superconductors in a strong-coupling regime

We analyze the possibility of the formation of a magnetic-field-induced insulating state in a two-dimensional granular superconductor with relatively strong intergranular coupling and show that such a state appears in a model with spatial variations of the single-grain critical magnetic field. This model describes realistic granular samples with a dispersion in grain sizes and explains the mech...

The strong Feller property for singular stochastic PDEs

We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

Explicit Representation of Strong Solutions of SDE’s driven by Infinite Dimensional Lévy Processes

We develop a white noise framework for Lévy processes on Hilbert spaces. As the main result of this paper, we then employ these white noise techniques to explicitly represent strong solutions of stochastic differential equations driven by a Hilbert-space-valued Lévy process.