Abstract
We consider compositions of stochastic processes that are governed by higherorder partial differential equations. The processes studied include compositions of Brownian motions, stable-like processes with Brownian time, Brownian motion whose time is an integrated telegraph process, and an iterated integrated telegraph process. The governing higher-order equations that are obtained are shown to be either of the usual parabolic type or, as in the last example, of hyperbolic type.
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Hochberg, K.J., Orsingher, E. Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations. J Theor Probab 9, 511–532 (1996). https://doi.org/10.1007/BF02214661
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DOI: https://doi.org/10.1007/BF02214661