کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1865472 1037838 2006 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Quadratic forms for Feynman–Kac semigroups
موضوعات مرتبط
مهندسی و علوم پایه فیزیک و نجوم فیزیک و نجوم (عمومی)
پیش نمایش صفحه اول مقاله
Quadratic forms for Feynman–Kac semigroups
چکیده انگلیسی

Some problems in a stochastic setting often involve the need to evaluate the Feynman–Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman–Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physics Letters A - Volume 353, Issue 6, 15 May 2006, Pages 446–451
نویسندگان
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