935 research outputs found
Stochastic ranking process with space-time dependent intensities
We consider the stochastic ranking process with space-time dependent jump
rates for the particles. The process is a simplified model of the time
evolution of the rankings such as sales ranks at online bookstores. We prove
that the joint empirical distribution of jump rate and scaled position
converges almost surely to a deterministic distribution, and also the tagged
particle processes converge almost surely, in the infinite particle limit. The
limit distribution is characterized by a system of inviscid Burgers-like
integral-partial differential equations with evaporation terms, and the limit
process of a tagged particle is a motion along a characteristic curve of the
differential equations except at its Poisson times of jumps to the origin
Diffusion processes in thin tubes and their limits on graphs
The present paper is concerned with diffusion processes running on tubular
domains with conditions on nonreaching the boundary, respectively, reflecting
at the boundary, and corresponding processes in the limit where the thin
tubular domains are shrinking to graphs. The methods we use are probabilistic
ones. For shrinking, we use big potentials, respectively, reflection on the
boundary of tubes. We show that there exists a unique limit process, and we
characterize the limit process by a second-order differential generator acting
on functions defined on the limit graph, with Kirchhoff boundary conditions at
the vertices.Comment: Published in at http://dx.doi.org/10.1214/11-AOP667 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
An improvement of the integrability of the state space of the Φ43-process and the support of the Φ43-measure constructed by the limit of stationary processes of approximating stochastic quantization equations
This is a remark paper for the Φ43 -measure and the associated flow on the torus which are constructed in [1] by the limit of the stationary processes of the stochastic quantization equations of approximation measures. We improve the integrability of the state space of the Φ43 -process and the support of the Φ43 -measure. For the improvement, we improve the estimates of the Hölder continuity in time of the solutions to approximation equations. In the present paper, we only discuss the estimates different from those in [1]
An improvement of the integrability of the state space of the -process and the support of the -measure constructed by the limit of stationary processes of approximating stochastic quantization equations
We improve the integrability of the state space of the -process
and the support of the -measure on the torus obtained in [Albeverio,
Kusuoka, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2020]. For the improvement,
we improve the estimates of the H\"older continuity in time of the solutions to
approximation equations. In the present paper, we only discuss the estimates
different from those in [Albeverio, Kusuoka, Ann. Sc. Norm. Super. Pisa Cl.
Sci. (5), 2020]
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