Abstract
The content of the preceding chapters was essentially devoted to the analysis of the first and second order moments of the state variable u = u(t,x,ω) at fixed values of the time t and space x variables. On the other hand, in the class of problems dealt with in this book, u is a time dependent random field and its behaviour can be properly described by its probability distribution as shown in the Appendix. This chapter deals with the analysis of the time-evolution of the probability densities associated to a dependent variable u at fixed values of the independent variables, i. e. time and space.
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Bellomo, N., Brzezniak, Z., de Socio, L.M. (1992). Time Evolution of the Probability Density. In: Nonlinear Stochastic Evolution Problems in Applied Sciences. Mathematics and Its Applications, vol 82. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1820-0_5
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DOI: https://doi.org/10.1007/978-94-011-1820-0_5
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