  Random Bridges have gained significant attention in recent years due to their
potential applications in various areas, particularly in information-based
asset pricing models. This paper aims to explore the potential influence of the
pinning point's distribution on the memorylessness and stochastic dynamics of
the bridge process. We introduce L\'evy bridges with random length and random
pinning points and analyze their Markov property. Our study demonstrates that
the Markov property of L\'evy bridges depends on the nature of the distribution
of their pinning points. The law of any random variables can be decomposed into
singular continuous, discrete, and absolutely continuous parts with respect to
the Lebesgue measure (Lebesgue's decomposition theorem). We show that the
Markov property holds when the pinning points' law does not have an absolutely
continuous part. Conversely, the L\'evy bridge fails to exhibit Markovian
behavior when the pinning point has an absolutely continuous part.
