scholarly journals Approximation rate in Wasserstein distance of probability measures on the real line by deterministic empirical measures

2021 ◽  
pp. 105684
Author(s):  
O. Bencheikh ◽  
B. Jourdain
Keyword(s):  
Real Line ◽  
Wasserstein Distance ◽  
Probability Measures ◽  
Approximation Rate ◽  
Empirical Measures ◽  
The Real

scholarly journals SAMPLING OF ONE-DIMENSIONAL PROBABILITY MEASURES IN THE CONVEX ORDER AND COMPUTATION OF ROBUST OPTION PRICE BOUNDS

2019 ◽  
Vol 22 (03) ◽  
pp. 1950002 ◽  
Author(s):  
AURÉLIEN ALFONSI ◽  
JACOPO CORBETTA ◽  
BENJAMIN JOURDAIN
Keyword(s):  
Real Line ◽  
Optimal Transport ◽  
Option Price ◽  
Order Moment ◽  
Probability Measures ◽  
Convex Order ◽  
Empirical Measures ◽  
The Real ◽  
Martingale Optimal Transport ◽  
Transport Problems

For [Formula: see text] and [Formula: see text] two probability measures on the real line such that [Formula: see text] is smaller than [Formula: see text] in the convex order, this property is in general not preserved at the level of the empirical measures [Formula: see text] and [Formula: see text], where [Formula: see text] (resp., [Formula: see text]) are independent and identically distributed according to [Formula: see text] (resp., [Formula: see text]). We investigate modifications of [Formula: see text] (resp., [Formula: see text]) smaller than [Formula: see text] (resp., greater than [Formula: see text]) in the convex order and weakly converging to [Formula: see text] (resp., [Formula: see text]) as [Formula: see text]. According to  Kertz & Rösler(1992) , the set of probability measures on the real line with a finite first order moment is a complete lattice for the increasing and the decreasing convex orders. For [Formula: see text] and [Formula: see text] in this set, this enables us to define a probability measure [Formula: see text] (resp., [Formula: see text]) greater than [Formula: see text] (resp., smaller than [Formula: see text]) in the convex order. We give efficient algorithms permitting to compute [Formula: see text] and [Formula: see text] (and therefore [Formula: see text] and [Formula: see text]) when [Formula: see text] and [Formula: see text] have finite supports. Last, we illustrate by numerical experiments the resulting sampling methods that preserve the convex order and their application to approximate martingale optimal transport problems and in particular to calculate robust option price bounds.

Probability measures with trivial Stam groups

1982 ◽  
Vol 91 (3) ◽  
pp. 477-484
Author(s):  
Gavin Brown ◽  
William Mohan
Keyword(s):  
Probability Measure ◽  
Real Number ◽  
Real Line ◽  
Probability Measures ◽  
The Real ◽  
Interesting Observation ◽  
Image Position ◽  
Positive Integers

Let μ be a probability measure on the real line ℝ, x a real number and δ(x) the probability atom concentrated at x. Stam made the interesting observation that eitheror else(ii) δ(x)* μn, are mutually singular for all positive integers n.

On the Duality between Coalescing Brownian Motions

2005 ◽  
Vol 57 (1) ◽  
pp. 204-224 ◽  
Author(s):  
Jie Xiong ◽  
Xiaowen Zhou
Keyword(s):  
Brownian Motion ◽  
Real Line ◽  
Joint Distribution ◽  
High Density ◽  
Brownian Motions ◽  
Empirical Measures ◽  
The Real ◽  
Density Limit

AbstractA duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.

scholarly journals The arithmetic of a semigroup of series of Walsh functions

2000 ◽  
Vol 68 (3) ◽  
pp. 365-378 ◽  
Author(s):  
I. P. Il'inskaya
Keyword(s):  
Real Line ◽  
Classical System ◽  
Convolution Semigroup ◽  
Probability Measures ◽  
Walsh Functions ◽  
Multiplicative Semigroup ◽  
Infinitely Divisible ◽  
The Real ◽  
Walsh Group ◽  
Series Of Functions

AbstractLet be the classical system of the Walsh functions, the multiplicative semigroup of the functions represented by series of functions Wk(t)with non-negative coefficients which sum equals 1. We study the arithmetic of . The analogues of the well-known [ related to the arithmetic of the convolution semigroup of probability measures on the real line are valid in . The classes of idempotent elements, of infinitely divisible elements, of elements without indecomposable factors, and of elements without indecomposable and non-degenerate idempotent factors are completely described. We study also the class of indecomposable elements. Our method is based on the following fact: is isomorphic to the semigroup of probability measures on the groups of characters of the Cantor-Walsh group.

Characterization theorems using conditional expectations

1975 ◽  
Vol 12 (02) ◽  
pp. 400-406
Author(s):  
Ignacy I. Kotlarski ◽  
William E. Hinds
Keyword(s):  
Real Line ◽  
Probability Measures ◽  
The Real ◽  
Conditional Expectations ◽  
Arbitrary Space ◽  
Characterization Theorems ◽  
Special Case

Recent characterizations of probability measures by use of conditional expectations have included many probability measures defined on subsets of the real line. This paper contains results which allow similar characterizations by use of conditional expectations but are valid for probability measures defined on subsets of an arbitrary space. In the special case of a measure defined on subsets of R' the result is not always as sharp as known results, but these theorems can be applied to measures defined on subsets of Rn with n ≧ 1.

Characterization theorems using conditional expectations

1975 ◽  
Vol 12 (2) ◽  
pp. 400-406 ◽  
Author(s):  
Ignacy I. Kotlarski ◽  
William E. Hinds
Keyword(s):  
Real Line ◽  
Probability Measures ◽  
The Real ◽  
Conditional Expectations ◽  
Arbitrary Space ◽  
Characterization Theorems ◽  
Special Case

Recent characterizations of probability measures by use of conditional expectations have included many probability measures defined on subsets of the real line. This paper contains results which allow similar characterizations by use of conditional expectations but are valid for probability measures defined on subsets of an arbitrary space. In the special case of a measure defined on subsets of R' the result is not always as sharp as known results, but these theorems can be applied to measures defined on subsets of Rn with n ≧ 1.

scholarly journals Sobolev inequalities for probability measures on the real line

2003 ◽  
Vol 159 (3) ◽  
pp. 481-497 ◽  
Author(s):  
F. Barthe ◽  
C. Roberto
Keyword(s):  
Real Line ◽  
Probability Measures ◽  
Sobolev Inequalities ◽  
The Real

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

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