Local time and Tanaka formula of G-martingales
نویسندگان
چکیده
منابع مشابه
Local Martingales in Discrete Time
For any discrete-time P–local martingale S there exists a probability measure Q ∼ P such that S is a Q–martingale. A new proof for this result is provided. This proof also yields that, for any ε > 0, the measure Q can be chosen so that dQ/dP ≤ 1 + ε.
متن کاملA Tanaka formula for the derivative of intersection local time in R 1
Abstract Let Bt be a one dimensional Brownian motion, and let α ′ denote the derivative of the intersection local time of Bt as defined in [3]. The object of this paper is to prove the following formula 1 2 αt(x) + 1 2 sgn(x)t = ∫ t 0 LBs−x s dBs − ∫ t 0 sgn(Bt −Bu − x)du (0.1) which was given as a formal identity in [3] without proof. Let B denote Brownian motion in R. In [3], Rosen demonstrat...
متن کاملContinuous Martingales and Local Martingales
Throughout these notes, (Ω,F ,P ) will be a probability space and F := {Ft }t∈J a filtration indexed by J , where J is an interval, usually J = [0,∞). The filtration F is said to be complete if each Ft contains all sets of measure 0, and is right-continuous if Ft =∩s>t Fs . A standard filtration is a filtration that is both complete and right-continuous. A stochastic process {X t }t≥0 defined o...
متن کاملBrownian motion, reflection groups and Tanaka formula
In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka’s formula for linear Brownian motion. The paper is closed with a description of the boun...
متن کاملChaotic Kabanov formula for the AzeÂma martingales
We derive the chaotic expansion of the product of nthand ®rst-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integral...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics-A Journal of Chinese Universities
سال: 2019
ISSN: 1005-1031,1993-0445
DOI: 10.1007/s11766-019-3622-4