Standard Brownian Motion
Tags: #Financial #EconomicsEquation
$$Z(t) \sim N(0, t) \\ Z(t+s) - Z(t) \sim N(0, s) \\ Z(t+s) \sim N(Z(t), s)$$Latex Code
Z(t) \sim N(0, t) \\
Z(t+s) - Z(t) \sim N(0, s) \\
Z(t+s) \sim N(Z(t), s)
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Introduction
Equation
Latex Code
Z(t) \sim N(0, t) \\
Z(t+s) - Z(t) \sim N(0, s) \\
Z(t+s) \sim N(Z(t), s)
Explanation
Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution
: Value of Z at time stamp t
: Stationary increments of Standard Brownian Motion
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