Stochastic solutions of a class of Higher order Cauchy problems in

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We study solutions of a class of higher order partial differential equations in bounded domains. These partial differential equations appeared first time in the papers of Allouba and Zheng allouba1, Baeumer, Meerschaert and Nane bmn-07, Meerschaert, Nane and Vellaisamy MNV, and Nane nane-h. We express the solutions by subordinating a killed Markov process by a hitting time of a stable subordinator of index 0<β<1, or by the absolute value of a symmetric α-stable process with 0<α≤ 2, independent of the Markov process. In some special cases we represent the solutions by running composition of k independent Brownian motions, called k-iterated Brownian motion for an integer k≥ 2. We make use of a connection between fractional-time diffusions and higher order partial differential equations established first by Allouba and Zheng allouba1 and later extended in several directions by Baeumer, Meerschaert and Nane bmn-07.