Parabolic Equations and Markov Processes Over p−adic Fields
نویسنده
چکیده
In this paper we construct and study a fundamental solution of Cauchy’s problem for p−adic parabolic equations of the type ∂u (x, t) ∂t + (f (D, β)u) (x, t) = 0, x ∈ Qnp , n ≥ 1, t ∈ (0, T ] , where f (D, β), β > 0, is an elliptic pseudo-differential operator. We also show that the fundamental solution is the transition density of a Markov process with state space Qp .
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