Some Asymptotic Estimates of Transition Probability Densities for Generalized Diffusion Processes with Self-similar Speed Measures | Zendy

Akira Iwatsuka | Zendy; Takahiko Fujita | Zendy

Open Access

Some Asymptotic Estimates of Transition Probability Densities for Generalized Diffusion Processes with Self-similar Speed Measures

Author(s) -

Akira Iwatsuka,

Takahiko Fujita

Publication year - 1990

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195170736

Subject(s) - mathematics , measure (data warehouse) , diffusion , diffusion process , operator (biology) , eigenvalues and eigenvectors , probability measure , borel measure , combinatorics , interval (graph theory) , boundary (topology) , mathematical analysis , string (physics) , differential operator , mathematical physics , quantum mechanics , physics , chemistry , knowledge management , biochemistry , innovation diffusion , repressor , database , computer science , transcription factor , gene

To a non-negative Borel measure dm(x) on an interval with suitable boundary conditions on the end points, we can associate a generalized differential operator A== -and a strong Markov process X on the support dm(x) dx of dm generated by the operator A. The measure dm is often called a string and the process X a generalized diffusion, also a quasi-diffusion or a gap diffusion, with the speed measure dm(x), cf. [9] for details. Let 0>^>/12>--be the eigenvalues of A= -and let ;?(r, x, y) be dm(x) dx the transition probability density of X with respect to dm(x). It was shown by M.G. Krein [10] and H.P. Mckean-D.B. Ray [12] that

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