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In this paper, by introducing a new type asymptotic coupling by reflection, we explore the long time behavior of random probability measure flows associated with a large class of one-dimensional McKean-Vlasov SDEs with common noise.…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Diffusion models do not recover semantic structure uniformly over time. Instead, samples transition from semantic ambiguity to class commitment within a narrow regime. Recent theoretical work attributes this transition to dynamical…
In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. The numerical approach is based on a triple decomposition of the flow variables into a steady mean,…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In…
We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions…
In the first part of the paper we develop the sensitivity analysis for the nonlinear McKean-Vlasov diffusions stressing precise estimates of growth of solutions and their derivatives with respect to the initial data, under rather general…
In this work, we consider the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations and examine some asymptotic behaviors of its strong solution. We establish the asymptotic log-Harnack inequality for the…
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients when the drift depends on time and space and is periodic in the time argument. There is no time…
We consider Mc Kean-Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs…
We establish the irreducibility of stochastic real Ginzburg-Landau equation with $\alpha$-stable noises by a maximal inequality and solving a control problem. As applications, we prove that the system converges to its equilibrium measure…
Existing training criteria in automatic speech recognition(ASR) permit the model to freely explore more than one time alignments between the feature and label sequences. In this paper, we use entropy to measure a model's uncertainty, i.e.…
We prove an equidistribution theorem a la Bader-Muchnik for operator-valued measures associated with boundary representations in the context of discrete groups of isometries of CAT(-1) spaces thanks to an equidistribution theorem of T.…
We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of…
We study the relations between (tight) logarithmic Sobolev inequalities, entropy decay and spectral gap inequalities for Markov evolutions on von Neumann algebras. We prove that log-Sobolev inequalities (in the non-commutative form defined…
We prove regularity and stochastic homogenization results for certain degenerate elliptic equations in nondivergence form. The equation is required to be strictly elliptic, but the ellipticity may oscillate on the microscopic scale and is…
A subthreshold signal is transmitted through a channel and may be detected when some noise -- with known structure and proportional to some level -- is added to the data. There is an optimal noise level, called stochastic resonance, that…