Some Properties Of Space-Time White Noise And Integral Theory

Research on stochastic partial differential equations is a very important part in stochastic analysis.We specialize to the space-time white noise which is an important class of random noise terms and consider several classes of stochastic partial differential equations driven by space-time white noise.After some preliminary background information for stochastic partial differential equations,we introduce the concept of space-time white noise and its properties,including sample function properties,Markov property and singularity.Then we introduce the stochastic integral for space-time white noise by developing the integration theory of martingale measure,since the space-time white noise is a kind of martingale measure.Finally we study some stochastic partial differential equations driven by space-time white noise.