Itô's theory of excursion point processes and its developments

DOI10.1016/j.spa.2010.01.012zbMath1201.60052OpenAlexW2066074304MaRDI QIDQ972810

Shinzo Watanabe

Publication date: 21 May 2010

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2010.01.012

zbMATH Keywords

excursion point processes associated with diffusion processes satisfying boundary conditionsstationary Poisson point process with values in function space

Mathematics Subject Classification ID

Diffusion processes (60J60) Stochastic integrals (60H05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (10)

The excursion measure away from zero for spectrally negative Lévy processes ⋮ Existence and uniqueness of the solutions of forward-backward doubly stochastic differential equations with Poisson jumps ⋮ Necessary and sufficient optimality conditions for relaxed and strict control of forward-backward doubly SDEs with jumps under full and partial information ⋮ Extensions of Brownian motion to a family of Grushin-type singularities ⋮ Infinite stable looptrees ⋮ Excursions of the Brox diffusion ⋮ Limit theorems of Brownian additive functionals ⋮ A limit theorem for trees of alleles in branching processes with rare neutral mutations ⋮ Itô's excursion theory and random trees ⋮ Brownian motion on stable looptrees

Cites Work

• Limit theorems for point processes and their functionals
• On the uniqueness of solutions of stochastic differential equations with singular drifts
• Excursion measure away from an exit boundary of one-dimensional diffusion processes
• Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line
• On the existence and uniqueness of diffusion processes with Wentzell's boundary conditions
• Time change approach to generalized excursion measures, and its application to limit theorems
• Semi-groupes de Feller sur une variété à bord compacte et problèmes aux limites intégro-différentiels du second ordre donnant lieu au principe du maximum
• Multi-dimensional diffusion and the Markov process on the boundary
• Brownian motions on a half line
• On stochastic differential equations
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