Brownian bridge process with Normal time slices
BrownianBridgeProcess[σ, {t1, a}, {t2, b}]
BrownianBridgeProcess[{t1, a}, {t2, b}]
BrownianBridgeProcess[t1, t2]
BrownianBridgeProcess[]
Mean[BrownianBridgeProcess[σ, {Subscript[t, 1], a}, {Subscript[t, 2], b}][t]]
→ (a*(-t + Subscript[t, 2]))/(-Subscript[t, 1] + Subscript[t, 2]) + (b*(t - Subscript[t, 1]))/(-Subscript[t, 1] + Subscript[t, 2])Variance[BrownianBridgeProcess[σ, {Subscript[t, 1], a}, {Subscript[t, 2], b}][t]]
→ (σ^2*(t - Subscript[t, 1])*(-t + Subscript[t, 2]))/(-Subscript[t, 1] + Subscript[t, 2])CovarianceFunction[BrownianBridgeProcess[σ, {Subscript[t, 1], a}, {Subscript[t, 2], b}], s, t]
→ (σ^2*(Min[s, t] - Subscript[t, 1])*(-Max[s, t] + Subscript[t, 2]))/(-Subscript[t, 1] + Subscript[t, 2])