2 6 N ov 2 00 4 The quantization complexity of diffusion processes by Steffen Dereich Technische
نویسنده
چکیده
In this article, we study the high resolution quantization problem for Rdvalued stochastic processes X that are solutions of stochastic differential equations. We let C([0, 1],Rd) denote the set of continuous functions mapping [0, 1] to Rd and denote by ‖·‖[0,1] the corresponding supremum norm, i.e. ‖f‖[0,1] = supt∈[0,1] |f(t)|. Analogously, Lq([0, 1],Rd) denotes the Lq-space of functions mapping [0, 1] to Rd and ‖ · ‖Lq [0,1] denotes the corresponding Lq-norm. We consider norm based distortion measures induced by the latter two norms. More precisely, for (E, ‖ · ‖) equal to (C([0, 1],Rd), ‖ · ‖[0,1]) or (Lq([0, 1],Rd), ‖ · ‖Lq [0,1]), we investigate the asymptotic behavior of the quantization error
منابع مشابه
High resolution quantization and entropy coding of jump processes
We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and correlated. We show in particular that in many cases entropy coding error and quantization error have distinct rates. Finally, we investigate the quantizatio...
متن کاملInfinite-dimensional Quadrature and Quantization
We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization of the underlying probability measure. In addition to the general setting we analyze in particular integration w.r.t. Gaussian measures and distributions of diffusion pro...
متن کاملar X iv : 0 80 4 . 13 11 v 3 [ nu cl - t h ] 6 N ov 2 00 8 Neutrino masses from the “ Darmstadt oscillations ”
Atominstitut der Österreichischen Universitäten, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Österreich, Stefan Meyer Institut für subatomare Physik, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090, Wien, Österreich, c Petersburg Nuclear Physics Institute, 188300 Gatchina, Orlova roscha 1, Russian Federation, Excellence Cluster Universe Technische U...
متن کاملTypical Distances in Ultrasmall Random Networks
We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1)) log logN − log(τ−2) , where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of ty...
متن کاملar X iv : 0 80 4 . 13 11 v 4 [ nu cl - t h ] 7 N ov 2 00 8 Neutrino masses from the “ Darmstadt oscillations ”
Atominstitut der Österreichischen Universitäten, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Wien, Österreich, Stefan Meyer Institut für subatomare Physik, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, A-1090, Wien, Österreich, c Petersburg Nuclear Physics Institute, 188300 Gatchina, Orlova roscha 1, Russian Federation, Excellence Cluster Universe Technische U...
متن کامل