Conditioned martingales
نویسندگان
چکیده
منابع مشابه
Conditioned Square Functions for Non-commutative Martingales
Abstract. We prove a weak-type (1,1) inequality involving conditioned square functions of martingales in non-commutative L-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the non-commutative Burkholder/Rosenthal inequalities from Ann. Probab. 31 (2003), 948-995. We also discuss BMO-norms of sums of non commuting order...
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 کاملMeasure-Free Martingales with Application to Classical Martingales
The aim of this work is to give a summary of some of the known properties of sets of measure-free martingales in vector lattices and Banach spaces. In particular, we consider the relationship between such sets of martingales and the ranges of the underlying filtration of conditional expectation operators.
متن کاملIndefinitely Oscillating Martingales
We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations for a given magnitude and show that this rate is asymptotically close to the theoretical upper bound. These bounds on probability and expectation of the number of upcrossings are compared to classical bounds from t...
متن کاملIntroduction to Martingales
We’ve already encountered and used martingales in this course to help study the hitting-times of Markov processes. Informally a martingale is simply a stochastic process Mt defined on some probability space (Ω,F ,P) that is “conditionally constant,” i.e., whose predicted value at any future time s > t is the same as its present value at the time t of prediction. The set T of possible indices t ...
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: Electronic Communications in Probability
سال: 2012
ISSN: 1083-589X
DOI: 10.1214/ecp.v17-1955