کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590104 | 1334933 | 2014 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Variational calculation of Laplace transforms via entropy on Wiener space and applications
ترجمه فارسی عنوان
محاسبه متغیر تبدیل لاپلاس از طریق آنتروپی در فضای وینر و برنامه های کاربردی
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کلمات کلیدی
معکوس آنتروپی، حساب ارزیابی، حسابداری مالایاین،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let (W,H,μ) be the classical Wiener space where H is the Cameron-Martin space which consists of the primitives of the elements of L2([0,1],dt)âRd. We denote by La2(μ,H) the equivalence classes w.r.t. dtÃdμ whose Lebesgue densities sâuË(s,w) are almost surely adapted to the canonical Brownian filtration. If f is a Wiener functional s.t. 1E[eâf]eâfdμ is of finite relative entropy w.r.t. μ, we prove thatJâ=infâ¡(Eμ[fâU+12|u|H2]:uâLa2(μ,H))â¥âlogâ¡Eμ[eâf]=infâ¡(â«Wfdγ+H(γ|μ):γâP(W)) where P(W) is the set of probability measures on (W,B(W)) and H(γ|μ) is the relative entropy of γ w.r.t. μ. We call f a tamed functional if the inequality above can be replaced with equality. We characterize the class of tamed functionals, which is much larger than the set of essentially bounded Wiener functionals. We show that for a tamed functional the minimization problem of l.h.s. has a solution u0 if and only if U0=IW+u0 is almost surely invertible anddU0μdμ=eâfEμ[eâf] and then u0 is unique. To do this, we prove the theorem which says that the relative entropy of U0μ is equal to the energy of u0 if and only if it has a μ-a.s. left inverse. We use these results to prove the strong existence of the solutions of stochastic differential equations with singular (functional) drifts and also to prove the non-existence of strong solutions of some stochastic differential equations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 267, Issue 8, 15 October 2014, Pages 3058-3083
Journal: Journal of Functional Analysis - Volume 267, Issue 8, 15 October 2014, Pages 3058-3083
نویسندگان
Ali Süleyman Ãstünel,