In this paper odd-order heat-type equations with different random initial conditions are examined. In particular, we give rigorous conditions for the existence of the solutions in the case where the initial condition is represented by a strictly $\varphi$-subGaussian harmonizable process $\eta=\eta(x)$. Also the case where $\eta$ is represented by a stochastic integral with respect to a process with independent increment is studied.
On the solutions of linear odd-order heat-type equations with random initial conditions / Beghin, Luisa; Y. U., Kozachenko; Orsingher, Enzo; L., Sakhno. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 127:4(2007), pp. 721-739. [10.1007/s10955-007-9309-x]
On the solutions of linear odd-order heat-type equations with random initial conditions
BEGHIN, Luisa;ORSINGHER, Enzo;
2007
Abstract
In this paper odd-order heat-type equations with different random initial conditions are examined. In particular, we give rigorous conditions for the existence of the solutions in the case where the initial condition is represented by a strictly $\varphi$-subGaussian harmonizable process $\eta=\eta(x)$. Also the case where $\eta$ is represented by a stochastic integral with respect to a process with independent increment is studied.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
