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Total Variation Distance
"... Abstract—We give explicit expressions, upper and lower bounds on the total variation distance between P and Q in terms of the distribution of the random variables log dP dQ (X) and log dP dQ (Y), where X and Y are distributed according to P and Q respectively. I. ..."
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Abstract—We give explicit expressions, upper and lower bounds on the total variation distance between P and Q in terms of the distribution of the random variables log dP dQ (X) and log dP dQ (Y), where X and Y are distributed according to P and Q respectively. I.
Trends to equilibrium in total variation distance
, 2008
"... This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling u ..."
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This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling
Bounds for Approximation in Total Variation Distance by Quantum Circuits
, 1995
"... It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate [5]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD) . TVD is ..."
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It was recently shown that for reasonable notions of approximation of states and functions by quantum circuits, almost all states and functions are exponentially hard to approximate [5]. The bounds obtained are asymptotically tight except for the one based on total variation distance (TVD) . TVD
On the Total Variation Distance of SemiMarkov Chains?
"... Abstract. SemiMarkov chains (SMCs) are continuoustime probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking probl ..."
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Abstract. SemiMarkov chains (SMCs) are continuoustime probabilistic transition systems where the residence time on states is governed by generic distributions on the positive real line. This paper shows the tight relation between the total variation distance on SMCs and their model checking
Total variation distance for Poisson subset numbers
 Ann. Comb
"... Abstract Let n be an integer and A 0 , . . . , A k random subsets of {1, . . . , n} of fixed sizes a 0 , . . . , a k , respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable W = ∩ k j=0 A j  ..."
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Abstract Let n be an integer and A 0 , . . . , A k random subsets of {1, . . . , n} of fixed sizes a 0 , . . . , a k , respectively chosen independently and uniformly. We provide an explicit and easily computable total variation bound between the distance from the random variable W = ∩ k j=0 A j
An invariance principle under the total variation distance.
 J. Theoret. Probab.,
, 2014
"... Abstract: Let X 1 , X 2 , . . . be a sequence of i.i.d. random variables, with mean zero and variance one and let S n = (X 1 + . . . + X n )/ √ n. An old and celebrated result of Prohorov ..."
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Abstract: Let X 1 , X 2 , . . . be a sequence of i.i.d. random variables, with mean zero and variance one and let S n = (X 1 + . . . + X n )/ √ n. An old and celebrated result of Prohorov
Improved lower bounds on the total variation distance for the Poisson approximation
 Statist. Probab. Lett
"... Abstract New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the ChenStein method. The new bounds rely on a nontrivial modification of the analysis by ..."
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Abstract New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the ChenStein method. The new bounds rely on a nontrivial modification of the analysis by
Exact Kolmogorov and total variation distances between some familiar discrete distributions
 Journal of Inequalities and Applications
"... We give exact closedform expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert W function. Copyright © 2006 J. A. Adell and P. Jo ..."
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We give exact closedform expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert W function. Copyright © 2006 J. A. Adell and P
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