Titlebook: Stochastic Processes in Quantum Physics; Masao Nagasawa Book 2000 Springer Basel AG 2000 Brownian motion.EFE.Lévy process.Markov property.

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Variational Principle for Relativistic Quantum Particles,ty measures. To show the absolute continuity between jump Markov processes, we will construct a multiplicative functional which is not of Kac type. With the help of the renormalization of the multiplicative functional, we will apply the stochastic variational principle to relativistic quantum particles.

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Time Dependent Subordination and Markov Processes with Jumps,r VIII. In this chapter we will solve the problem, extending Bochner’s subordination to temporally inhomogeneous Markov processes, and generalizing the Feynman-Kac formula to the time-dependent (-inhomogeneous) subordinate processes.

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,Concave Majorants of Lévy Processes and the Light Cone, They escape from the light cone immediately after starting. Nonetheless, it is expected that there exists critical time after which the movement of a quantum particle will be confined in the light cone. To see this, taking one dimensional Lévy processes, we look at their concave majorants (vertex processes).[.

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of the bottom boundary layer, just in front of the dipole. If a step occurs at the bottom in the channel output, a single vortex will be formed, the dipole becomes a part of a structure having a horseshoe shape. In a periodic driving flow, after a while this structure results in a dipole and a spanw

epidermis

Masao Nagasawajet injected at the top wall, are analyzed. The numerical study is carried out for a Reynolds number of 500 with different Richardson and Prandtl numbers. A hot plate is provided on the bottom of the cavity which generates the heating of the fluid. In order to investigate the effect of the length of

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Masao Nagasawaof the bottom boundary layer, just in front of the dipole. If a step occurs at the bottom in the channel output, a single vortex will be formed, the dipole becomes a part of a structure having a horseshoe shape. In a periodic driving flow, after a while this structure results in a dipole and a spanw

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