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https://doi.org/10.1007/978-1-4757-1665-8Markov process; Martingal; Semimartingal; Semimartingale; functional analysis; mathematical statistics; obWater-Brash 发表于 2025-3-22 03:07:22
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Introduction,A considerable number of problems in the statistics of random processes are formulated within the following scheme.EXALT 发表于 2025-3-22 15:33:43
Essentials of probability theory and mathematical statistics,According to Kolmogorov’s axiomatics the primary object of probability theory is the . space (Ω, .). Here (Ω, .) denotes measurable space, i.e., a set Ω consisting of elementary events ., with a distinguished system . of its subsets (events), forming a .-algebra, and . denotes a probability measure (probability) defined on sets in ..tangle 发表于 2025-3-22 18:19:16
Martingales and semimartingales: discrete time,Let (Ω, ℱ, .) be a probability space, and let . be a nondecreasing family of sub-.-algebras ℱ.figurine 发表于 2025-3-23 01:16:43
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The Wiener process, the stochastic integral over the Wiener process, and stochastic differential eqLet (Ω, ., .) be a probability space and . = (. .), . ≥ 0, be a Brownian motion process (in the sense of the definition given in Section 1.4). Denote . .= .{.: . ., . ≤ .}. Then, according to (1.30) and (1.31), (P-a.s.) ., ..JECT 发表于 2025-3-23 08:31:47
Square integrable martingales, and structure of the functionals on a Wiener process,Let (Ω, ℱ, .) be a complete probability space, and let . = (ℱ.), . ≥ 0, be a nondecreasing (right continuous) family of sub-.-algebras ℱ, each of which is augmented by sets from ℱ having zero .-probability.