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Diffusions: Basic Properties,he velocity of the fluid at the point x at time t, then a reasonable mathematical model for the position X. of the particle at time t would be a stochastic differential equation of the form . where W. ∈ ℝ. denotes “white noise” and .(t, x) ∈ ℝ.. The Ito interpretation of this equation is . where B.换话题 发表于 2025-3-22 05:06:57
Application to Stochastic Control,ownian motion. Here u ∈ R. is a parameter whose value we can choose at any instant in order to control the process X. · Thus u=u(t,ω) is a stochastic process. Since our decision at time t must be based upon what has happened up to time t, the function ω→u(t,ω) must (at least) be measurable wrt. ..,傲慢物 发表于 2025-3-22 09:21:34
Application to Stochastic Control,i.e. the process u. must be ..-adapted. Thus the right hand side of (11.1) is well-defined as a stochastic integral, under suitable assumptions on b and σ. At the moment we will not specify the conditions on b and a further, but simply assume that the process X. satisfying (11.1) exists. See further comments on this in the end of this chapter.名义上 发表于 2025-3-22 16:31:56
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Springer-Verlag Berlin Heidelberg 1989Intruder 发表于 2025-3-22 23:56:05
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https://doi.org/10.1007/978-3-662-02574-1Brownian motion; Differential Equations; Equations; Optimal Filtering; Stochastic Control; Stochastic cal