Determining the First Probability Density Function of Linear Random Initial Value Problems by the Random Variable Transformation (RVT) Technique: A Comprehensive Study

Figure 1

Plot of 𝑓₁(𝑧,𝑡) given by (35) in Example 10 at different values of 𝑡={0,0.25,0.5,0.75,…,2} (corresponding to the solid lines) in the case that 𝑍₀∼𝑁(𝜇=0;𝜎²=1), 𝑡₀=0, and 𝑎=−1.