scholarly journals Lower Tail Probability Estimates for Subordinators and Nondecreasing Random Walks

1987 ◽  
Vol 15 (1) ◽  
pp. 75-101 ◽  
Author(s):  
Naresh C. Jain ◽  
William E. Pruitt
Keyword(s):  
Random Walks ◽  
Tail Probability ◽  
Lower Tail ◽  
Probability Estimates ◽  
Lower Tail Probability

scholarly journals On the Lower Tail Variational Problem for Random Graphs

2016 ◽  
Vol 26 (2) ◽  
pp. 301-320 ◽  
Author(s):  
YUFEI ZHAO
Keyword(s):  
Variational Problem ◽  
Random Graph ◽  
Random Graphs ◽  
Large Deviation ◽  
Tail Probability ◽  
Edge Density ◽  
Lower Tail ◽  
Lower Tail Probability ◽  
Large Deviation Problem ◽  
Deviation Problem

We study the lower tail large deviation problem for subgraph counts in a random graph. Let XH denote the number of copies of H in an Erdős–Rényi random graph $\mathcal{G}(n,p)$. We are interested in estimating the lower tail probability $\mathbb{P}(X_H \le (1-\delta) \mathbb{E} X_H)$ for fixed 0 < δ < 1.Thanks to the results of Chatterjee, Dembo and Varadhan, this large deviation problem has been reduced to a natural variational problem over graphons, at least for p ≥ n−αH (and conjecturally for a larger range of p). We study this variational problem and provide a partial characterization of the so-called ‘replica symmetric’ phase. Informally, our main result says that for every H, and 0 < δ < δH for some δH > 0, as p → 0 slowly, the main contribution to the lower tail probability comes from Erdős–Rényi random graphs with a uniformly tilted edge density. On the other hand, this is false for non-bipartite H and δ close to 1.

Resampling Permutation Probability Values for Six Measures of Qualitative Variation

2007 ◽  
Vol 104 (3) ◽  
pp. 773-776 ◽  
Author(s):  
Janis E. Johnston ◽  
Kenneth J. Berry ◽  
Paul W. Mielke
Keyword(s):  
Tail Probability ◽  
Fortran Program ◽  
Test Statistics ◽  
Test Statistic ◽  
Lower Tail ◽  
Qualitative Variation ◽  
Data Table ◽  
Kendall’S Τ ◽  
Lower Tail Probability

An algorithm and associated FORTRAN program are provided for six common measures of ordinal association: Kendall's τ a and τ b, Stuart's τ c, Goodman and Kruskal's γ, and Somers' dyx and dxy. Program ROMA reports the observed data table, the values for the six test statistics, and the resampling upper- and lower-tail probability values associated with each test statistic.

Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations

2018 ◽  
Vol 05 (02) ◽  
pp. 1850016
Author(s):  
Nian Yao
Keyword(s):  
Large Deviation ◽  
Garch Model ◽  
Tail Probability ◽  
Deviation Probability ◽  
Leverage Ratio ◽  
Probability Estimates ◽  
Volatility Models ◽  
Optimal Leverage ◽  
Model Inverse ◽  
Leveraged Etfs

In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.

scholarly journals The volume and time comparison principle and transition probability estimates for random walks

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
András Telcs
Keyword(s):  
Random Walks ◽  
Transition Probability ◽  
Exit Time ◽  
Sufficient Conditions ◽  
Probability Estimates ◽  
Mean Exit Time ◽  
International Audience ◽  
The Mean ◽  
Necessary And Sufficient ◽  
Upper Estimate

International audience This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the mean exit time from a ball are independent of the center, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is given if the mean exit time is independent of the center but the volume is not.

Non-homogeneous Random Walks

2016 ◽  
Author(s):  
Mikhail Menshikov ◽  
Serguei Popov ◽  
Andrew Wade
Keyword(s):  
Random Walks
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