Ikeda, N. & Watanabe, S. (1989). Stochastic Di erential Equations and Di usion Processes, Vol. 24, 2 edn, North-Holland Publ. Co., Amsterdam. Home/Search Document Not in Database Summary Related Articles Check |
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Simulating Constrained Animal Motion Using Stochastic.. - Brillinger (Correct)
.... B(t) denote a bivariate Brownian motion. Given the functional parameters and ## consider the equation dr(t) r(t) t)dt ##(r(t) t)dB(t) 2) Conditions for the existence and uniqueness of solutions may be found in Bhattacharya and Waymire [4] Stroock and Varadhan [30] and Ikeda and Watanabe [13] for example. To tie in with the material of the previous sectionitmaybethecasethat (r,t) #H(r,t) for some H . The motion of r(t) may be periodic, for example when there is a seasonal or circadian e#ect. The motion may be bounded. The parameters and ## may include explanatories, e.g. ....
....They may walk along it for a while. They may run at it and bounce back. They may stand there for a while. This relates to the character of the reflections implicit in the simulation method employed. Dupuis and Ishii [10] allow di#erent types of reflections, including oblique. Ikeda and Watanabe [13] allow sticky and non sticky behavior at the boundary. 6 Some simulations To get practical experience, some elementary simulations were carried out. A naive boundary, namely a circle was employed to make obtaining the result of a projection easy. Figure 4 shows results for the three ....
IKEDA, N. and WATANABE, S. (1989). Stochastic Di#erential Equations and Di#usion Processes. North-Holland, Amsterdam.
Integrated Brownian motion, conditioned to be positive - Groeneboom, Jongbloed.. (1999) (Correct)
....is transient; i.e. U(t) # =1. Proof. We prove the existence of a unique strong solution to (5.1) by a localization argument. Let, for N 0, the function c N be defined by c N (x, y) c(x#1 N , y ( N ) Then c N is globally Lipschitz. Hence it follows from Theorem 3.1, p. 164, Chapter IV, [3] that the system dU(t) V(t)dt, dV (t) c N( U(t) V(t) dt dW (t) has a unique strong solution (UN ,V N ) for each N 0. Moreover, UN ,V N ) is a solution of the original system up to time TN = inf t 0:U N( t) 1 N or VN (t) N . Pasting these solutions yields a solution ( V) to the system ....
Ikeda, N., and Watanabe, S. (1981). Stochastic Di#erential Equations and Di#usion Processes. North-HollandKodansha, Amsterdam and Tokyo.
Multivariate Fractionally Integrated CARMA Processes - Marquardt (2006) (Correct)
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Ikeda, N. & Watanabe, S. (1989). Stochastic Di erential Equations and Di usion Processes, Vol. 24, 2 edn, North-Holland Publ. Co., Amsterdam.
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