My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 2nd, 2009, 12:00 PM   #1
Newbie
 
Joined: Apr 2009

Posts: 1
Thanks: 0

martingale crossing probability

Helle everybody,

I was reading through a proof within a paper and found one fact I could not explain myself:
We have a stochastic process (X_t); t>=0 and X_t is a martingale, It is said in the paper that "it is a well-known fact that the probability that a martingale with initial position y (X_0 = y) , defined on a state space (0,l), will ever hit zero, is 1- y/l"
--> P(inf{X_s: 0<=s<=\infinity} = 0) = 1- y/l.
Unfortunately I could not find any similar facts in the literature. Maybe somebody can give me some hints.
Thanks forward!
Brainyboy is offline  
 
April 22nd, 2009, 07:31 AM   #2
Newbie
 
Joined: Apr 2009

Posts: 1
Thanks: 0

Re: martingale crossing probability

Hint : Express with respect to condition and its complementary event and use optional sampling theorem
TheBridge is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
crossing, martingale, probability



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Crossing the desert uzurpatorul Math Events 8 April 26th, 2017 04:15 PM
Martingale mathmari Advanced Statistics 0 May 21st, 2013 10:23 AM
Crossing a desert (alternative) mathsman Math Events 7 July 25th, 2011 09:25 AM
Martingale Problem j_bloggs Advanced Statistics 0 March 15th, 2010 12:35 AM
martingale elenaas Applied Math 0 October 13th, 2009 01:03 PM





Copyright © 2019 My Math Forum. All rights reserved.