The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.
The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.
In this paper, we prove a large deviation principle for a class of stochastic Cahn-Hilliard partial differential equations driven by space-time white noises.
Ke Hua SHI Dan TANG Yong Jin WANGSchool of Mathematical Sciences, Nankai University, Tianjin 300071, P. R. China
In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method.
We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a continuity modulus of the solution, and the HSlder continuity is presented.
In this paper, we start at a random evolution system on biological particles, which is described by a Markov jump system. Under a suitable scaling, we perform a proper approximation procedure. Then the so-called weak convergence of Markov processes and Martingales allow us to establish a （deterministic） two species competitive Lotka-Volterra equation.
The authors explore a class of jump type Cahn-Hilliard equations with fractional noises. The jump component is described by a (pure jump) Lévy space-time white noise. A fixed point scheme is used to investigate the existence of a unique local mild solution under some appropriate assumptions on coefficients.
