Stochastic Partial Differential Equations, Space-time White Noise and Random Fields

Stochastic Partial Differential Equations, Space-time White Noise and Random Fields

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This open access book provides a comprehensive introduction to the theory of stochastic partial differential equations (SPDEs). The focus is on SPDEs driven by Gaussian space-time white noise. The book covers both linear and nonlinear SPDEs, with Lipschitz and locally Lipschitz coefficients and multiplicative noise.  It provides a modern presentation of the theory of stochastic integration with respect to space-time white noise and unifies many results in the literature. The book discusses fundamental topics such as existence and uniqueness of random field solutions, along with their spac...