A question for stochastic calculus

Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the symbol ^ in the context of stochastic calculus, specifically as referenced in a book by Shreve. Participants explore various meanings and notations associated with this symbol.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant notes that the symbol ^ appears as a logical conjunction operator in the book.
  • Another participant suggests it may represent a wedge product, expressing uncertainty.
  • A different participant proposes that in this context, k^t could mean min(k,t), relating it to the infimum in a partially ordered set.
  • Concerns are raised about the variety of notations and the potential confusion it causes for learners.

Areas of Agreement / Disagreement

Participants express differing interpretations of the symbol ^, with no consensus reached on its meaning.

Contextual Notes

There is a noted lack of clarity regarding the definitions and notations used in stochastic calculus, which may contribute to the confusion among participants.

tennishaha
Messages
21
Reaction score
0
The attachment is from Shreve's stochastic calculus book

In the attachment what does the symbol ^ mean?

Thanks
 

Attachments

  • pic08.jpg
    pic08.jpg
    7.1 KB · Views: 550
Physics news on Phys.org
It may be a wedge product, I am not sure :confused:
 
I've compared a couple of different books and it seems k^t means min(k,t) in this context. It is from the lattice of partially ordered set, and means infimum (greatest lower bound). Also known as the 'meet' of the elements in partially ordered set.
Someone should really clarify this please as I am getting curious as to why there are so many different notations and total disregard for the average mind
 

Similar threads

Undergrad Question about ARMA process: Changing a Stochastic Process into a Transfer Function
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Stochastic calculus: Ito's lemma and differentials
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Stopping Time in layman's words
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Are Chaotic and Stochastic processes related?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Karhunen–Loève theorem expansion random variables
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad About stochastic differential equation and probability density
  • · Replies 1 ·
Replies
1
Views
2K
Graduate The name of the process underlying distributons with a hazard rate
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Stochastic differential equations with time uncertainty....
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Probability of a Stochastic Markov process
  • · Replies 1 ·
Replies
1
Views
2K
Insights Brownian Motions and Quantifying Randomness in Physical Systems
  • · Replies 1 ·
Replies
1
Views
10K