创造性
发表于 2025-3-25 06:25:55
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NIP
发表于 2025-3-25 10:59:50
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Immortal
发表于 2025-3-25 15:18:34
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Innocence
发表于 2025-3-25 18:56:55
,Reminiscences of some of Paul Lévy’s ideas in Brownian Motion and in Markov Chains,We begin with a resume. Let {. ≥ 0} be a semigroup of stochastic matrices with elements p.(., where . is a countable set, satisfying the condition .. It is known that .(0) = . exists and . The state . is called . if . < +∞, and . if . = +∞ (Lévy’s terminology). The matrix .) is called . when equality holds in (3) for all ..
HPA533
发表于 2025-3-25 20:26:27
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constellation
发表于 2025-3-26 01:49:32
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GOUGE
发表于 2025-3-26 07:48:33
The Independence of Hitting Times and Hitting Positions to Spheres for Drifted Brownian Motions,A drifted Brownian motion X. is a diffusion process on .. whose infinitesimal generator has the form . where ... is the usual Laplace operator and . is a smooth vector field on ... When b ≡ 0, X. becomes the usual n-dimensional Brownian motion.
先行
发表于 2025-3-26 08:35:41
A Maximal Inequality,Let X be a uniformly integrable, cadlag non-negative regular supermartingale. Such a process X has the representation . where A. is continuous and increasing on the half open interval [0,∞), A. = 0 and A may assign mass to ∞ which is just A. - A. where .. Then we have the maximal inequality.
受人支配
发表于 2025-3-26 12:42:13
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过去分词
发表于 2025-3-26 19:46:55
Right Brownian Motion and Representation of Initial Problem,Let {.: t > 0} be the right Brownian motion on [0, ∞) determined by the transition density: for . ∈ [0,∞). . This is a Markov process having the tendency moving to the right direction. 0 can be a starting point, but is never reached, i.e., {0} is a polar set.