The Generalized Feller Equation And Related Topics (Monographs and Surveys in Pure and Applied Mathematics)

"The Generalized Feller Equation and Related Topics", a summary account of this subject, deals with a particular Fokker-Planck equation and with its solutions and their structure. The source solution and certain singular solutions are of primary interest. The diffusion and drift coefficients depend on the space variable by power laws and on four parameters. Important related equations are derived. The source solution is used in the construction of integral transform initial conditions and series solutions. Certain singular solutions are used as convolution kernels to construct bundary conditions. Bounded and positive solutions are discussed. The book also deals with probability density functions which arise from the source solution as stationary states of the underlying dynamic evolution processes from completely concentrated initial states. The associated parameter estimation problems are addressed. The generalized Feller equation has been established as a mathematical model for a variety of diffusion-type processes in physics, chemistry and electronics. Both as a text and as a reference, it should prove useful to applied mathematicians, scientists, engineers and statisticians working in the field of diffusion processes.