abstract 89
Bulletin of Computational Applied Mathematics (Bull CompAMa)Â
89
Random evolutions, telegraph and Klein-Gordon equations, and Brownian motion (Research Paper)
Henryk Gzyl
Here we provide a probabilistic way to compute the transition probabilities of the telegraph process. For that, we review a connection between random evolutions, the telegraph and the Klein-Gordon equations. This equation appears when one decouples the two equations that determine the transition probability of the telegraph process. Next we show how to integrate the Klein-Gordon equation by invoking a Brownian motion process. This connection comes up after the transformation of the hyperbolic initial value problem either into an elliptic problem by means of a Laplace transform, or into a parabolic problem by means of a transmutation operator.
Keywords: Random evolutions; telegraph equation; Klein-Gordon equation; Brownian motion; transmutation operators.
Cite this paper:
Gzyl H.
Random evolutions, telegraph and Klein-Gordon equations, and Brownian motion
Bull. Comput. Appl. Math. (Bull CompAMa)
Vol. 12, No.1 pp.35-46, 2024.