Mathematics > Probability
[Submitted on 2 Jan 2022 (v1), last revised 9 Oct 2022 (this version, v8)]
Title:Pseudorandom Vector Generation Using Elliptic Curves And Applications
View PDFAbstract:In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of i.i.d. random variables, with values in the hypercube $[0,1]^d$ with uniform distribution. As an application, we obtain, in the discrete time simulation, an efficient algorithm to simulate, uniformly distributed sample path sequence of a sequence of independent standard Wiener processes. This could be employed for use, in the full history recursive multi-level Picard approximation method, for numerically solving the class of semilinear parabolic partial differential equations of the Kolmogorov type.
Submission history
From: Chung-Pang Mok [view email][v1] Sun, 2 Jan 2022 13:21:49 UTC (14 KB)
[v2] Thu, 20 Jan 2022 02:54:21 UTC (14 KB)
[v3] Mon, 24 Jan 2022 03:08:50 UTC (14 KB)
[v4] Mon, 7 Feb 2022 02:55:08 UTC (15 KB)
[v5] Tue, 5 Apr 2022 11:45:22 UTC (16 KB)
[v6] Mon, 11 Apr 2022 08:05:33 UTC (21 KB)
[v7] Mon, 16 May 2022 12:18:41 UTC (21 KB)
[v8] Sun, 9 Oct 2022 01:11:53 UTC (22 KB)
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