Time reversal of infinite-dimensional diffusions

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Continuous Time Perpetuities and the Time Reversal of Diffusions

Infinite–dimensional Diffusions as Limits of Random Walks on Partitions

The present paper originated from our previous study of the problem of harmonic analysis on the infinite symmetric group S∞. This problem leads to a family {Pz} of probability measures, the z–measures, which depend on the complex parameter z ∈ C. The z–measures live on the Thoma simplex, an infinite–dimensional compact space Ω which is a kind of dual object to the group S∞. The aim of the paper...

Exponential Ergodicity and Raleigh-schrödinger Series for Infinite Dimensional Diffusions

, with η ∈ T d , where the coefficients ai, bi are finite range, bounded with bounded second order partial derivatives and the ellipticity assumption infi,η ai(η) > 0 is satisfied. We prove that whenever ν is an invariant measure for this diffusion satisfying the logarithmic Sobolev inequality, then the dynamics is exponentially ergodic in the uniform norm, and hence ν is the unique invariant m...

Time Reversal of Diffusions' by U. G. Haussmann And

It is shown that if a diffusion process, {Xt: 0 < t < 1}, on Rd satisfies dXt = b(t, Xt) dt + a(t, Xt) dwt then the reversed process, {Xt: 0 < t < 1} where Xt = Xl t , is again a diffusion with drift b and diffusion coefficient a, provided some mild conditions on b, a, and p(, the density of the law of X(, hold. Moreover b and a are identified. 1. Introduction. It is well known that a Markov pr...