Jump telegraph processes and financial markets with memory.
Telegraph models of financial markets.
Branching random motions, nonlinear hyperbolic systems and travellind waves
A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal...
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