Related papers: Shifted Composition I: Harnack and Reverse Transpo…
We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for…
Coupling arguments are a central tool for bounding the deviation between two stochastic processes, but traditionally have been limited to Wasserstein metrics. In this paper, we apply the shifted composition rule--an information-theoretic…
We establish a dimension-free, uniform-in-time reverse transportation inequality for Langevin dynamics with non-convex potentials. This inequality controls the R\'enyi divergence of arbitrary order between the process distributions starting…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
Information measures can be constructed from R\'enyi divergences much like mutual information from Kullback-Leibler divergence. One such information measure is known as Sibson $\alpha$-mutual information and has received renewed attention…
We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case…
Recently, optimal transport-based approaches have gained attention for deriving counterfactuals, e.g., to quantify algorithmic discrimination. However, in the general multivariate setting, these methods are often opaque and difficult to…
This paper deals with the distributed order time-fractional diffusion equations with non-homogeneous Dirichlet (Nuemann) boundary condition. We first prove the wellposedness of the weak solution to the initial boundary value problem for the…
This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…
In this work we introduce a family of transformations, named \textit{divergence transformations}, interpolating between any pair of probability density functions sharing the same support. We prove the remarkable property that the whole…
This work examines a class of switching jump diffusion processes. The main effort is devoted to proving the maximum principle and obtaining the Harnack inequalities. Compared with the diffusions and switching diffusions, the associated…
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a uniform parabolicity condition. As the main…
In this paper, we focus on a space-time fractional diffusion equation with the generalized Caputo's fractional derivative operator and a general space nonlocal operator (with the fractional Laplace operator as a special case). A weak…
In this article we derive Talagrand's $T_2$ inequality on the path space w.r.t. the maximum norm for various stochastic processes, including solutions of one-dimensional stochastic differential equations with measurable drifts, backward…
We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
By the method of coupling and Girsanov transformation, Harnack inequalities [F.-Y. Wang, 1997] and strong Feller property are proved for the transition semigroup associated with the multivalued stochastic evolution equation on a Gelfand…
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry,…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
In this paper we develop a time reversal method for the radiative transport equation to solve two problems: an inverse problem for the recovery of an initial condition from boundary measurements, and the exact boundary controllability of…