Convex densities and their financial applications
Convex entropy decay via the Bochner–Bakry–Emery approach
We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known results...
Convex hulls, Sticky particle dynamics and Pressure-less gas system
We introduce a new condition which extends the definition of sticky particle dynamics to the case of discontinuous initial velocities with negative jumps. We show the existence of a stochastic process and a forward flow satisfying and , where is the law of and is the velocity of particle at time . Results on the flow characterization and Lipschitz continuity are also given.Moreover, the map is the entropy solution of a scalar conservation law where the flux represents the particles...
Convex orderings for stochastic processes
We consider partial orderings for stochastic processes induced by expectations of convex or increasing convex (concave or increasing concave) functionals. We prove that these orderings are implied by the analogous finite dimensional orderings.
Convex rearrangements of Lévy processes
In this paper we study asymptotic behavior of convex rearrangements of Lévy processes. In particular we obtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measure is regularly varying at + with exponent α ∈ (1,2).
Convexités uniformes et inégalités de martingales.
Convexity at infinity and Brownian motion on manifolds with unbounded negative curvature.
Convexity inequalities for estimating generalized conditional entropies from below
Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional -entropy and two kinds of non-extensive conditional -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...
Convexity of measures in certain convex cones in vector space ...-algebras.
Convolution de mesures portées par une surface convexe
Convolution powers of spread-out probabilities
Convolution property and exponential bounds for symmetric monotone densities
Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 < k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
Convolution Semigroups and Generalized Telegraph Equations.
Convolution Semigroups and Resolvent Families of Measures on Hypergroups.
Convolution Semigroups of Local Type.
Convolutional attractors of stationary sequences of random measures on compact groups
Convolutions of probability measures on semigroups.
Copolymer at selective interfaces and pinning potentials : weak coupling limits
We consider a simple random walk of length N, denoted by (Si)i∈{1, …, N}, and we define (wi)i≥1 a sequence of centered i.i.d. random variables. For K∈ℕ we define ((γi−K, …, γiK))i≥1 an i.i.d sequence of random vectors. We set β∈ℝ, λ≥0 and h≥0, and transform the measure on the set of random walk trajectories with the hamiltonian λ∑i=1N(wi+h)sign(Si)+β∑j=−KK∑i=1Nγij1{Si=j}. This transformed path measure describes an hydrophobic(philic) copolymer interacting with a layer of width 2K around an interface...
Copula and semicopula transforms.
Copulas with given values on a horizontal and a vertical section
In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented.