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Let (X(t)) (t ≥ 0) be a semi-Markov diffusion process. The process (J(T )) (T ≥ 0) equal to the integral of (X(t)) on interval [0, T ) is studied.… Click to show full abstract
Let (X(t)) (t ≥ 0) be a semi-Markov diffusion process. The process (J(T )) (T ≥ 0) equal to the integral of (X(t)) on interval [0, T ) is studied. The relation between one-dimensional differential equation of the second order of elliptical type and asymptotics of a solution to Dirichlet problem on an interval with length tending to zero is established. This relation is used to derive a differential equation for the Laplace transform of the semi-Markov generating function of the process (J(t)).
Keywords:
process;
semi markov;
diffusion process;
markov diffusion
Journal Title: Journal of Mathematical Sciences
Year Published: 2018
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Journal Title: Journal of Mathematical Sciences
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!