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Distributions of Sojourn Time, Maximum and Minimum for Pseudo-Processes Governed by Higher-Order Heat-Type Equations
The higher-order heat-type equation $ \partial u/\partial t=\pm\partial^{n} u/ \partial x^{n} $ has been investigated by many authors. With this equation is associated a pseudo-process $(X_t)_{t\ge 0}$ which is governed by a signed measure. In the even-order case, Krylov (1960) proved that the classical arc-sine law of Paul Levy for …