# Trouble understanding Notation in Stochastic Calculus (wedge symbol ∧)

I am a beginner in Stochastic Calculus. I am having trouble understanding the meaning behind a specific notation which appears in the topic of Ito process which in differential notation can be written as

$$dX(t)=\mu (t)dt+\sigma (t)dW(t)$$

Now it is mentioned as a fact that if $$X(0)$$, $$\mu (t)$$ and $$\sigma (t)$$ are deterministic functions then $$X(t)$$ is a Gaussian Process with mean and covariance functions given by

$$m(t)=X(0)+\int_{0}^{t}\mu (s)ds$$, $$c(t_{1},t_{2})=\int_{0}^{t_{1}\land t_{2}}\sigma (s)^{2}ds$$

I have trouble understanding the upper limit of the integrand appearing the covariance function i.e. $$t_{1}\land t_{2}$$. What does that mean logically?

• The wedge symbol $\wedge$ is used to represent minimum, whilst $\vee$ is used to represent the maximum. So $t_1 \wedge t_2=\min \left(t_1,t_2 \right)$ Mar 29 '20 at 14:31
• Thanks a lot for clarifying. Mar 29 '20 at 15:45
• One gimmick I use to remember it, is that $\wedge$ looks like the letter A, you can read it as "And", and logical And can be implemented as the minimum of two Boolean variables. Mar 30 '20 at 14:32

Many financial math (stochastic calculus) books use $$\wedge$$ to mean minimum: $$a \wedge b = \min(a,b)$$ and likewise $$\vee$$ to mean maximum: $$a \vee b = \max(a,b)$$ This notation is actually not immediately recognized even by some math people outside finance. It is sort of consistent with $$\wedge$$ denoting conjunction or infimum and $$\vee$$ denoting disjunction or supremum.
Personally, I would have preferred to use dyadic floor and ceiling that the language APL used to use: $$a⌊b = \min(a,b)$$ and likewise $$a ⌈ b = \max(a,b)$$. But no one uses that.