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- W2949964470 abstract "We consider different types of processes obtained by composing Brownian motion $B(t)$, fractional Brownian motion $B_{H}(t)$ and Cauchy processes $% C(t)$ in different manners. We study also multidimensional iterated processes in $mathbb{R}^{d},$ like, for example, $left( B_{1}(|C(t)|),...,B_{d}(|C(t)|)right) $ and $left( C_{1}(|C(t)|),...,C_{d}(|C(t)|)right) ,$ deriving the corresponding partial differential equations satisfied by their joint distribution. We show that many important partial differential equations, like wave equation, equation of vibration of rods, higher-order heat equation, are satisfied by the laws of the iterated processes considered in the work. Similarly we prove that some processes like $% C(|B_{1}(|B_{2}(...|B_{n+1}(t)|...)|)|)$ are governed by fractional diffusion equations." @default.
- W2949964470 created "2019-06-27" @default.
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- W2949964470 date "2010-08-05" @default.
- W2949964470 modified "2023-09-26" @default.
- W2949964470 title "Equations of Mathematical Physics and Compositions of Brownian and Cauchy processes" @default.
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