Sep 2026· Theory of Stochastic Processes· Vol 30(46), pp. 15-32· 0 citations
Abstract
We study evolutions of measures under flows of solutions to stochastic differential equations with interaction. Under suitable regularity
assumptions on the coefficients, we prove moment bounds for the compact-set Jacobian norm. These bounds yield pathwise transfer of logarithmic
Sobolev, concentration, and Talagrand transport inequalities from the initial measure to the random pushforward measure at time t.
Finally, for a kernel model satisfying a pairwise dissipativity
condition, we prove exponential decay of the expected dispersion around the random center of mass.
For diffusions whose coefficients are smooth, with at most linear growth and bounded derivatives of higher order, we establish explicit pointwise bounds on the spatial derivatives of the classical solution to the Cauchy problem with polynomially growing initial data. We also obtain explicit growth estimates for the der...
We study the fundamental solution operators associated to Kolmogorov equations with symmetric non-local diffusion with rough kernels. We prove that these operators are induced by measurable kernels and prove sharp upper bounds in terms of a kinetic profile governed by the interplay of transport and non-local diffusion....
We establish the local boundedness of time derivatives of bounded viscosity solutions to the normalized parabolic $p$-Laplace equation for every $p\in(1,\infty)$. The proof combines a logarithmic Bernstein argument with quantitative stability to derive a recursive estimate between different regularizations. For $p=1$ a...
We study a linear backward stochastic partial differential equation with unbounded observation-adapted random coefficients, motivated by the duality approach to nonlinear filtering. The coefficients depend predictably on the observation history through a control with almost surely finite time-integrated squared norm. T...
Jie Xiong, Wen Xu, Zuo-Quan Xu et al.· 0 citations
The present work investigates the existence and uniqueness of solutions for a fractional stochastic differential equations with $\psi$-Caputo fractional derivatives. We establish important theoretical conclusion and examine the energy growth bounds and asymptotic behavior of the stochastic solution using the Banach's f...
R. Hariharan, R. Udhayakumar· Journal of the Indonesian Ma...· 0 citations
The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entrop...
Noah Geltner, Ansgar Jungel· 0 citations
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