相关论文: Gaussian integrability of distance function under …

The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…

The goal of this paper is to understand the conditional law of a stochastic process once it has been observed over an interval. To make this precise, we introduce the notion of a continuous disintegration: a regular conditional probability…

This paper is devoted to one-dimensional interpolation Gagliardo-Nirenberg-Sobolev inequalities. We study how various notions of duality, transport and monotonicity of functionals along flows defined by some nonlinear diffusion equations…

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many…

Extending the approach of the paper [Mathieu, P. (1997) Hitting times and spectral gap inequalities, Ann. Inst. Henri Poincare 33, 4, 437 -- 465], we prove that the Poincare inequality for a (possibly non-symmetric) Markov process yields…

Given a parabolic cylinder $Q =(0,T)\times\Omega$, where $\Omega\subset \mathbb{R}^{N}$ is a bounded domain, we prove new properties of solutions of \[ u_t-\Delta_p u = \mu \quad \text{in $Q$} \] with Dirichlet boundary conditions, where…

Let $(X_t)$ be a reflected diffusion process in a bounded convex domain in $\mathbb R^d$, solving the stochastic differential equation $$dX_t = \nabla f(X_t) dt + \sqrt{2f (X_t)} dW_t, ~t \ge 0,$$ with $W_t$ a $d$-dimensional Brownian…

Empirically defining some constant probabilistic orbits of f(x) and g(x) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open…

We give necessary integral conditions and sufficient ones for the existence of a general concept of $\mu$-dichotomy for evolution operators defined on the half-line which includes as particular cases the well-known concepts of nonuniform…

We investigate when the local Lipschitz property of the real-valued function $g(z) = d_Y (f(z),A)$ implies the global Lipschitz property of the mapping $f:X\to Y$ between the metric spaces $(X,d_X)$ and $(Y,d_Y)$. Here, $d_Y(y,A)$ denotes…

Non-Gaussian concentration estimates are obtained for invariant probability measures of reversible Markov processes. We show that the functional inequalities approach combined with a suitable Lyapunov condition allows us to circumvent the…

McDonald and Clerk [Phys.\ Rev.\ Research 5, 033107 (2023)] showed that for linear open quantum systems the Liouvillian spectrum is independent of the noise strength. We first make this noise-independence principle precise in continuous…

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…

We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform…

In this paper we consider an ergodic diffusion process with jumps whose drift coefficient depends on $\mu$ and volatility coefficient depends on $\sigma$, two unknown parameters. We suppose that the process is discretely observed at the…

We consider symmetric Markov chains on $\Bbb Z^d$ where we do {\bf not} assume that the conductance between two points must be zero if the points are far apart. Under a uniform second moment condition on the conductances, we obtain upper…

We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that…

In this article we derive moment estimates, exponential integrability, concentration inequalities and exit times estimates for canonical diffusions in two settings each beyond the scope of Riemannian geometry. Firstly, we consider…

We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real normed linear space X under a proximinality condition on K. We do not assume the uniform…

We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…