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Probability: Theory and examples
 CAMBRIDGE U PRESS
, 2011
"... Some times the lights are shining on me. Other times I can barely see. Lately it occurs to me what a long strange trip its been. Grateful Dead In 1989 when the first edition of the book was completed, my sons David and Greg were 3 and 1, and the cover picture showed the Dow Jones at 2650. The last t ..."
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Cited by 1331 (16 self)
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twenty years have brought many changes but the song remains the same. The title of the book indicates that as we develop the theory, we will focus our attention on examples. Hoping that the book would be a useful reference for people who apply probability in their work, we have tried to emphasize
Probability Theory
, 2006
"... This paper introduces some elementary notions in MeasureTheoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers. Finally, the notions of conditional expectation and cond ..."
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This paper introduces some elementary notions in MeasureTheoretic Probability Theory. Several probabalistic notions of the convergence of a sequence of random variables are discussed. The theory is then used to prove the Law of Large Numbers. Finally, the notions of conditional expectation
Probability Theory
"... The goal of Probability Theory is to quantify our degree of uncertainness. Probability Theory and Statistics, that is based on Probability Theory and uses its language, have applications to almost all Sciences and humain activities. The basic object of study of Probability Theory are random objects ..."
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The goal of Probability Theory is to quantify our degree of uncertainness. Probability Theory and Statistics, that is based on Probability Theory and uses its language, have applications to almost all Sciences and humain activities. The basic object of study of Probability Theory are random objects
and Probability Theory
, 2012
"... Analysis of commercial and free and open source solvers for linear optimization problems ..."
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Cited by 2 (0 self)
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Analysis of commercial and free and open source solvers for linear optimization problems
The analogues of entropy and of Fisher’s information measure in free probability theory
 I. Comm. Math. Phys
, 1993
"... Dedicated to Huzuhiro Araki Abstract. Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the CramerRao inequality are proved. ..."
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Cited by 254 (12 self)
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Dedicated to Huzuhiro Araki Abstract. Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the CramerRao inequality are proved.
Probability Theory
, 1991
"... Summary. We study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by spacetime white noise. The nonlinearity appears both in the drift and in the diffusion coefficient. Roughly speaking, at any point (t, x) where the solutio ..."
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Summary. We study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by spacetime white noise. The nonlinearity appears both in the drift and in the diffusion coefficient. Roughly speaking, at any point (t, x) where the solution u(t, x) is strictly positive it obeys the equation, and at a point (t, x) where u(t, x) is zero we add a force in order to prevent it from becoming negative. This can be viewed as an extension both of onedimensional SDEs reflected at 0, and of deterministic variational inequalities. Existence of a minimal solution is proved. The construction uses a penalization argument, a new existence theorem for SPDEs whose coefficients depend on the past of the solution, and a comparison theorem for solutions of whitenoise driven SPDEs.
Probability Theory As Logic
, 1990
"... At the 1988 workshop we called attention to the "Mind Projection Fallacy" which is present in all fields that use probability. Here we give a more complete discussion showing why probabilities need not correspond to physical causal influences, or "propensities" affecting mass phe ..."
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Cited by 75 (0 self)
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phenomena. Probability theory is far more useful if we recognize that probabilities express fundamentally logical inferences pertaining to individual cases. We note several examples of the difference this makes in real applications.
Probability theory refresher
, 2007
"... Probability theory is nothing but common sense reduced to calculation. — Pierre Laplace, 1812 ..."
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Probability theory is nothing but common sense reduced to calculation. — Pierre Laplace, 1812
HOMOTOPY PROBABILITY THEORY I
"... ABSTRACT. This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework p ..."
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Cited by 3 (2 self)
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ABSTRACT. This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework
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