One-Sided Characterization of the Normal Distribution in the Set of Infinitely Divisible Distributions

1982 ◽  
Vol 26 (2) ◽  
pp. 392-399 ◽  
Author(s):  
H.-J. Rossberg ◽  
G. Siegel
Keyword(s):  
Normal Distribution ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

AN APPLICATION OF THE SEGAL–BARGMANN TRANSFORM TO THE CHARACTERIZATION OF LÉVY WHITE NOISE MEASURES

2010 ◽  
Vol 13 (02) ◽  
pp. 191-221 ◽  
Author(s):  
YUH-JIA LEE ◽  
HSIN-HUNG SHIH
Keyword(s):  
White Noise ◽  
Probability Measures ◽  
Infinitely Divisible Distributions ◽  
Infinite Dimensions ◽  
Infinitely Divisible ◽  
Tempered Distributions ◽  
Bargmann Transform ◽  
Second Moment ◽  
Lévy White Noise

Being inspired by the observation that the Stein's identity is closely connected to the quantum decomposition of probability measures and the Segal–Bargmann transform, we are able to characterize the Lévy white noise measures on the space [Formula: see text] of tempered distributions associated with a Lévy spectrum having finite second moment. The results not only extends the Stein and Chen's lemma for Gaussian and Poisson distributions to infinite dimensions but also to many other infinitely divisible distributions such as Gamma and Pascal distributions and corresponding Lévy white noise measures on [Formula: see text].

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

A note on passage times and infinitely divisible distributions

1967 ◽  
Vol 4 (2) ◽  
pp. 402-405 ◽  
Author(s):  
H. D. Miller
Keyword(s):  
Random Walk ◽  
Markov Process ◽  
Continuous Time ◽  
Random Variables ◽  
Independent Random Variables ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible ◽  
Time Intervals ◽  
Mutually Independent ◽  
Passage Times

Let X(t) be the position at time t of a particle undergoing a simple symmetrical random walk in continuous time, i.e. the particle starts at the origin at time t = 0 and at times T1, T1 + T2, … it undergoes jumps ξ1, ξ2, …, where the time intervals T1, T2, … between successive jumps are mutually independent random variables each following the exponential density e–t while the jumps, which are independent of the τi, are mutually independent random variables with the distribution . The process X(t) is clearly a Markov process whose state space is the set of all integers.

Sign in / Sign up

Export Citation Format

Share Document