Titlebook: Seminar on Stochastic Processes, 1983; E. Çinlar,K. L. Chung,R. K. Getoor Book 1984 Springer Science+Business Media New York 1984 ALS.ASP.

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,Ray-Knight’s Theorem on Brownian Local Times and Tanaka’s Formula,Using Tanaka’s formula in an appropriate filtration, we give a representation property for the excursions below a given level of the (possibly killed) Brownian motion. Ray-Knight’s theorems on Brownian local times are then directly deduced from Tanaka’s formula.

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Regularity Properties of a Stochastic Partial Differential Equation,This article is a sequel to [8] which studied the electrical potential in a randomly-stimulated neuron of the brain or spinal chord by means of the stochastic partial differential equation . where W̊ is a space-time white noise. The neuron was represented by a line segment, and V(x,t) was the electrical potential at x at time t.

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1050-6977 such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The previous two seminars were held at Northwesterr. University, Evanston. This one was held at the University of Florida, Gainesville. The invited participants in th

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Construction of Right Processes from Hitting Distributions,pace K as above. (See [2].) It is well known that such a process is determined, up to a (random) time change, by its hitting distributions of compact sets of the state space. Our problem is therefore to construct a right process on K with prescribed hitting distributions H.(x,·) for all compact D ⊂ K and x ∈ K.

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Local Times and Quantum Fields,e quantum field theory. The isomorphism theorem allows one to express moments of the cutoff P(ϕ). fields in terms of multiple local times for the Brownian motion. On the other hand, techniques of field theory can be applied to investigate local times and self-crossing properties of Markov processes.

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Approximation of Debuts,ve functions. We show that for each A ∈ ε. and each finite measure u on the state space, there is a decreasing sequence (G.) of finely open, ε.-measurable supersets of A such that . P.-a.s. We deduce this result from a similar one which applies also to suitable non-Markov processes.

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