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• W2766674548 abstract "Author(s): Mahboubi, Pejman | Advisor(s): Liggett, Thomas | Abstract: In recent decades, as a result of mathematicians' endeavor to come up with more realistic models for complex phenomena, the acceptance of a stochastic model seemed inevitable. One class of these models are Stochastic Partial Differential Equations (SPDEs).The solution to a SPDE, considered as a Wiener functional, can be analyzed by means of Malliavin calculus. Malliavin calculus, which is a calculus on the Wiener space, is becoming a standard method for investigating the existence of the density of random variables. In this thesis, we study nonlinear SPDEs of the form partial_t u(t,x)=L u(t,x)+f(u(t,x)) w, with a periodic boundary condition on a torus, where L is the generator of a Levy process on the torus. We used the technique of Malliavin calculus to show that when asigma is smooth, under a mild condition on L, the law of the solution has a density with respect to Lebesgue measure for all tg0 and x in the torus. It turns out that the density of u(t,x) has an upper bound that is independent of x. We also prove that the Malliavin derivatives grow in time with an exponential rate. This result, in certain cases, extends to the weak intermittency of the random field of the Malliavin derivatives." @default.
• W2766674548 created "2017-11-10" @default.
• W2766674548 creator A5005285555 @default.
• W2766674548 date "2012-01-01" @default.
• W2766674548 modified "2023-09-27" @default.
• W2766674548 title "Intermittency of the Malliavin Derivatives and Regularity of the Densities for a Stochastic Heat Equation" @default.
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• W2766674548 hasPublicationYear "2012" @default.
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