节约
发表于 2025-3-23 13:15:53
Probability and Stochastic Processes for Physicists978-3-030-48408-8Series ISSN 2198-7882 Series E-ISSN 2198-7890
observatory
发表于 2025-3-23 16:53:04
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我们的面粉
发表于 2025-3-23 20:37:47
DistributionsWe will explore now the protocols used to define on . a probability . also called either . or ., and we will start with finite or countable spaces so that . will be defined in an elementary way.
Freeze
发表于 2025-3-23 23:40:52
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PRO
发表于 2025-3-24 06:02:13
Limit TheoremsThe Limit Theorems are statements about limits of sequences of sums of .’s when the number of addenda grows to infinity.
哎呦
发表于 2025-3-24 08:21:53
General NotionsThe notion of stochastic process (.). on a probability space . with . has already been introduced in the Section. where we pointed out that it can be considered from two complementary standpoints.
你敢命令
发表于 2025-3-24 14:13:54
Dynamical Theory of Brownian MotionIn 1930 L.S. Ornstein and G.F. Uhlenbeck [.] addressed again the problem of elaborating a suitable model for the Brownian motion, and they refined in more detail the Langevin dynamical equation to investigate the phenomenon at time scales shorter than those considered by Einstein [.] and Smoluchowski [.] in 1905-6.
使害怕
发表于 2025-3-24 15:15:35
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防锈
发表于 2025-3-24 22:45:21
Nicola Cufaro PetroniBuilds a bridge between physics and probability.Explains the role of Brownian motion in physics.Includes appendices devoted to particular details, calculations and concise treatments of thought-provok
弯腰
发表于 2025-3-25 00:27:38
Heuristic Definitionsabilistic properties. This illuminating and informative procedure, however, can not be easily replicated for other typical, non trivial processes whose trajectories, as we will see later, can only be defined either as limits of suitable approximations or by adopting a more general standpoint