Standard Brownian Motion Equation Formula Latex Code and Summary

Standard Brownian Motion

Tags: #Financial #Economics

Equation

$$Z(t) \sim N(0, t) \\ Z(t+s) - Z(t) \sim N(0, s) \\ Z(t+s) \sim N(Z(t), s)$$

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

$Z(t) \sim N(0, t) \\ Z(t+s) - Z(t) \sim N(0, s) \\ Z(t+s) \sim N(Z(t), s)$

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)

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

$Z(t)$ : Value of Z at time stamp t
$Z(t+s) - Z(t)$ : Stationary increments of Standard Brownian Motion

Discussion

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Donna Thompson

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2023-02-14 00:00
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Ralph Ward reply to Donna Thompson

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2023-02-20 00:00:00.0
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Randy Murphy

If I could have one wish, it would be to pass this exam.

2024-01-26 00:00
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Heather Adams reply to Randy Murphy

Nice~

2024-02-24 00:00:00.0
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Gabriel Simmons

The only thing I want is to pass this test.

2023-02-03 00:00
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Brian Clark reply to Gabriel Simmons

Nice~

2023-02-21 00:00:00.0
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