A question for stochastic calculus

[tennishaha]

The attachment is from Shreve's stochastic calculus book

In the attachment what does the symbol ^ mean?

Thanks

 

[cronxeh]

Well your attachment is still pending approval, but fear not, citizen! I have this book and I've searched through it and in every instance the logical conjunction operator ^ appears.

http://en.wikipedia.org/wiki/Logical_conjunction

 

[cronxeh]

It may be a wedge product, I am not sure

 

[cronxeh]

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 :grumpy:

 

[CellCoree]

for your question about stochastic calculus. The symbol ^ in the attachment represents the exponentiation operator. In other words, it is used to raise a number or variable to a power. For example, 2^3 would represent 2 raised to the power of 3, which is equal to 8. In the context of stochastic calculus, this symbol is often used to represent the exponent of a stochastic process, which is a key concept in this field. I hope this helps clarify the use of the ^ symbol in the attachment.