A Stochastic Differential Equation for a Class of Feller's One‐dimensional Diffusion | Zendy

Groh Jürgen | Zendy

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A Stochastic Differential Equation for a Class of Feller's One‐dimensional Diffusion

Author(s) -

Groh Jürgen

Publication year - 1982

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19821070122

Subject(s) - mathematics , stochastic differential equation , diffusion , mathematical analysis , diffusion process , operator (biology) , differential equation , space (punctuation) , measure (data warehouse) , state space , class (philosophy) , markov process , diffusion equation , order (exchange) , innovation diffusion , statistics , philosophy , economy , repressor , database , artificial intelligence , service (business) , knowledge management , chemistry , linguistics , computer science , biochemistry , transcription factor , thermodynamics , physics , finance , economics , gene

A class of one‐dimensional continuous strong Markovian processes is considered. Such process X were first described by William Feller in a purely analytical way, using the generalized second‐order differential operator D m D p + . In the case of natural boundaries of the state space R and a trivial road map p (x)= x, these diffusion processes are martingales. In the present paper it is additionally assumed that the speed measure m contains a nonvanishing absolutely continous component. Then a stochastic differential equation is derived, which has the diffusion X as a weak solution.

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