کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1156926 | 958896 | 2010 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Itô’s stochastic calculus and Heisenberg commutation relations
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Stochastic calculus and stochastic differential equations for Brownian motion were introduced by K. Itô in order to give a pathwise construction of diffusion processes. This calculus has deep connections with objects such as the Fock space and the Heisenberg canonical commutation relations, which have a central role in quantum physics. We review these connections, and give a brief introduction to the noncommutative extension of Itô’s stochastic integration due to Hudson and Parthasarathy. Then we apply this scheme to show how finite Markov chains can be constructed by solving stochastic differential equations, similar to diffusion equations, on the Fock space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 120, Issue 5, May 2010, Pages 698–720
Journal: Stochastic Processes and their Applications - Volume 120, Issue 5, May 2010, Pages 698–720
نویسندگان
Philippe Biane,