interrupt 发表于 2025-3-25 04:33:35
Brownian Local Times,Consider the standard .ianmotion D and recall the associated differential operator . =D. / 2 acting on D(.) = C. (R.).exacerbate 发表于 2025-3-25 10:20:52
http://reply.papertrans.cn/28/2791/279015/279015_22.pngIntervention 发表于 2025-3-25 12:00:09
Generators,A particle starts at time . = 0 at -1 ≤ . < 0, moving at speed +1 until it hits . = 0; at that moment, it begins a reflecting B.ian motion on [0, + ∞), stopping at the passage time m. to . = 1, waiting at that place for an exponential holding time e with mean and jumping at time m. + e to the point ∞.柏树 发表于 2025-3-25 16:29:54
A general view of diffusion in several dimensions,Given a (conservative) diffusion D on a space . as described in 7.1, its generator . can be expressed in terms of the hitting probabilities and mean exit times.for open D⊂Q via E. B. Dynkin’s formula . to borrow a phrase of W. Feller’s,Polydipsia 发表于 2025-3-25 21:27:53
http://reply.papertrans.cn/28/2791/279015/279015_25.png最低点 发表于 2025-3-26 00:24:46
978-3-540-60629-1Springer-Verlag Berlin Heidelberg 1996Pamphlet 发表于 2025-3-26 04:37:29
http://reply.papertrans.cn/28/2791/279015/279015_27.pngGEON 发表于 2025-3-26 10:39:36
Time changes and killing,ntial operator .• of degree ≦2 expressed in terms of . (scale, speed measure, . via the formulas 4.1.8) and each invariant has a simple probabilistic meaning embodied in the formulas 4.1.7) .HEW 发表于 2025-3-26 16:21:26
Local and inverse local times,taining 0 as an inside point or as a left end point, with — .(0) + .(0) (.)(0) = 0 in the second case. A number of the statements made below hold for transient diffusions also (see esp. 6.3, 6.5, 6.6); the necessary modifications of the proofs are left to the reader.新陈代谢 发表于 2025-3-26 20:10:01
Brownian motion in several dimensions,g as . is compact or not, let C. be the space of bounded continuous functions .: . ⋃ ∞ → . with .(∞) ≡ 0 , introduce the (continuous) . with . and .(+∞) ≡ ∞, define ., ., and . . and .m+ as usual, take . ∈ .) with the usual properties including P∞ ., and call the associated motion ..1) and 2) are not Unrelated.