The nearest neighbor random walk on subspaces of a vector space and rate of convergence

1995 ◽  
Vol 8 (2) ◽  
pp. 321-346 ◽  
Author(s):  
Anthony J. D'Aristotile
Keyword(s):  
Random Walk ◽  
Vector Space ◽  
Rate Of Convergence ◽  
Nearest Neighbor

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (04) ◽  
pp. 733-740
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn (x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G ∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (4) ◽  
pp. 733-740 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn(x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

scholarly journals ASPECT BASED SENTIMENT ANALYSIS DATA KUESIONER DI RUMAH SAKIT MUHAMMADIYAH LAMONGAN MENGGUNAKAN ALGORITMA K-NN.

JOUTICA ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 506
Author(s):  
Mustain Mustain Mustain
Keyword(s):  
Vector Space ◽  
Sentiment Analysis ◽  
Nearest Neighbor ◽  
Vector Space Model ◽  
Analysis Data ◽  
Cosine Similarity ◽  
K Nearest Neighbor ◽  
Space Model

Kesulitan untuk mengorganisir data kuesioner yang bersifat konvensional melatarbelakangi penelitian ini. Oleh karena itu dibuat sistem yang memudahkan pengelompokan data kuesioner secara otomatis yang lengkap dengan sentimen yang terkandung didalamnya. Dataset yang digunakan dalam penelitian ini adalah data kuesioner rumah sakit Muhammadiyah lamongan. Penelitian ini hanya menangani kuesioner yang berbentuk teks. Data dengan fisik kertas direkap kemudian diinput ke database lengkap dengan kategori unit kerja dan sentiment. Selanjutnya dataset tersebut di dilakukan pre-prosesing yang meliputi penanganan negasi case folding, tokenizing, filtering dan stemming. Sebagai data uji komentar dari kuesioner akan dilakukan pre-prosesing selanjutnya dihitung tingkat kemiripan document dengan menggunakan metode K- Nearest Neighbor dan Vector Space Model. Jumlah data yang ditangani mempengaruhi performa system terutama dari akurasi dan kecepatan pada saat proses klasifikasi. Hasil dari sistem yang dibuat berupa ranking dokumen yang paling mirip dengan dataset berdasarkan urutan nilai cosine similarity. Ujicoba klasifikasi berdasarkan kelas kategori menghasilkan nilai akurasi 91 %. Ujicoba berdasarkan Kelas Sentimen sebesar 94 %.dari kombinasi keduanya system berhasil mendapat akurasi sebesar 86 %

scholarly journals A Comprehensive Comparative Study Using Vector Space Model with K-Nearest Neighbor on Text Categorization Data

2007 ◽  
Vol 2 (1) ◽  
pp. 14-22 ◽  
Author(s):  
Wa`el Musa Hadi ◽  
Fadi Thabtah ◽  
Salahideen Mousa ◽  
Samer Al Hawari ◽  
Ghassan Kanaan ◽  
...  
Keyword(s):  
Comparative Study ◽  
Vector Space ◽  
Text Categorization ◽  
Nearest Neighbor ◽  
Vector Space Model ◽  
K Nearest Neighbor ◽  
Space Model

scholarly journals The Rate of Convergence of a Random Walk to Brownian Motion

1973 ◽  
Vol 1 (4) ◽  
pp. 699-701 ◽  
Author(s):  
David F. Fraser
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Rate Of Convergence

scholarly journals Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020 ◽  
Vol 52 (3) ◽  
pp. 735-771
Author(s):  
Christel Geiss ◽  
Céline Labart ◽  
Antti Luoto
Keyword(s):  
Differential Equation ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Backward Stochastic Differential Equation ◽  
Stochastic Equations ◽  
Terminal Condition ◽  
Probabilistic Methods ◽  
Mean Square ◽  
Finite Difference Equations ◽  
Backward Sdes

AbstractLet (Y, Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk $B^n$ from the underlying Brownian motion B by Skorokhod embedding, one can show $L_2$-convergence of the corresponding solutions $(Y^n,Z^n)$ to $(Y, Z).$ We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in $C^{2,\alpha}$. The proof relies on an approximative representation of $Z^n$ and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to the approximating stochastic equations. We derive these properties by probabilistic methods.

The exponential rate of convergence of the distribution of the maximum of a random walk

1975 ◽  
Vol 12 (02) ◽  
pp. 279-288 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Exponential Convergence ◽  
Random Variables ◽  
Limiting Distribution ◽  
Partial Sums ◽  
Exponential Rate ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence

Let Gn (x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under conditions, typical for complete exponential convergence, the decay of Gn (x) — G(x) is asymptotically equal to c.H(x)n −3/2 γn as n → ∞ where c and γ are known constants and H(x) is a function solely depending on x.

scholarly journals Local and Global Survival for Nonhomogeneous Random Walk Systems on Z

2014 ◽  
Vol 46 (01) ◽  
pp. 256-278 ◽  
Author(s):  
Daniela Bertacchi ◽  
Fábio Prates Machado ◽  
Fabio Zucca
Keyword(s):  
Random Walk ◽  
Nearest Neighbor ◽  
Sufficient Conditions ◽  
Local Extinction ◽  
Active Particle ◽  
Translation Invariant ◽  
Local Survival ◽  
Global Survival ◽  
Starting Location ◽  
The Right

We study an interacting random walk system on ℤ where at time 0 there is an active particle at 0 and one inactive particle on each site n ≥ 1. Particles become active when hit by another active particle. Once activated, the particle starting at n performs an asymmetric, translation invariant, nearest neighbor random walk with left-jump probability l n . We give conditions for global survival, local survival, and infinite activation both in the case where all particles are immortal and in the case where particles have geometrically distributed lifespan (with parameter depending on the starting location of the particle). More precisely, once activated, the particle at n survives at each step with probability p n ∈ [0, 1]. In particular, in the immortal case, we prove a 0-1 law for the probability of local survival when all particles drift to the right. Besides that, we give sufficient conditions for local survival or local extinction when all particles drift to the left. In the mortal case, we provide sufficient conditions for global survival, local survival, and local extinction (which apply to the immortal case with mixed drifts as well). Analysis of explicit examples is provided: we describe completely the phase diagram in the cases ½ - l n ~ ± 1 / n α, p n = 1 and ½ - l n ~ ± 1 / n α, 1 - p n ~ 1 / n β (where α, β &gt; 0).

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