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Main Authors:	Angiuli, Luciana, Ferrari, Simone
Format:	Preprint
Published:	2026
Subjects:	Analysis of PDEs Probability Primary: 60B11. Secondary: 28C20, 46G12, 47D03, 47D07, 60G51, 60H15, 60J35
Online Access:	https://arxiv.org/abs/2603.25177
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Smoothing on $L^1$ for ground state transformed semigroups in non-local settings
by: Baraniewicz, Miłosz, et al.
Published: (2026)

Evolutionary semigroups on path spaces
by: Denk, Robert, et al.
Published: (2024)

Decay of resolvent kernels and Schrödinger eigenstates for Lévy operators
by: Kaleta, Kamil, et al.
Published: (2025)

Limit theorems for the generator of a symmetric Levy process with the delta potential
by: Abildaev, Temirlan
Published: (2025)

Mosco convergence of gradient forms with non-convex interaction potential
by: Grothaus, Martin, et al.
Published: (2021)

Quasi-ergodic theorems for Feynman-Kac semigroups and large deviation for additive functionals
by: Kim, Daehong, et al.
Published: (2024)

Additive subordination of multiparameter Markov processes
by: D'Onofrio, Giuseppe, et al.
Published: (2025)

Abstract Formulation of Mean-Field Models and Propagation of Chaos
by: Lim, Tau Shean, et al.
Published: (2025)

On the Cauchy Problem for the Dispersion Generalized Camassa-Holm Equation
by: Ayhan, Nesibe, et al.
Published: (2023)

Rearranged Stochastic Heat Equation
by: Delarue, François, et al.
Published: (2022)

Regularity theory for a new class of fractional parabolic stochastic evolution equations
by: Kirchner, Kristin, et al.
Published: (2022)

Sharp bounds for non-trace class noise and applications to SPDEs
by: Agresti, Antonio, et al.
Published: (2026)

Martingales and Path-Dependent PDEs via Evolutionary Semigroups
by: Denk, Robert, et al.
Published: (2025)

Stochastic evolution equations driven by arbitrary cylindrical Lévy processes
by: Bodó, Gergely, et al.
Published: (2026)

Quasi-ergodicity of compact strong Feller semigroups on $L^2$
by: Kaleta, Kamil, et al.
Published: (2023)

Non-symmetric Lévy-type operators
by: Minecki, Jakub, et al.
Published: (2021)

Analytic and stochastic description of Brownian motions on star graphs
by: Bobrowski, Adam, et al.
Published: (2025)

On Portenko's approximation of skew Brownian motion
by: Bobrowski, Adam, et al.
Published: (2026)

Functional calculus on weighted Sobolev spaces for the Laplacian on the half-space
by: Lindemulder, Nick, et al.
Published: (2024)

A Generalization of Lévy's Theorem on Positive Matrix Semigroups
by: Gerlach, Moritz
Published: (2024)

Weighted Helmholtz--Hodge decompositions, Lyapunov functions, and invariant measures
by: Lee, Haesung, et al.
Published: (2026)

Bakry-Emery Curvature of the Fractional Laplacian via Fractional Brownian Covariance
by: Fontes, Ramiro
Published: (2026)

An $L_{q}(L_{p})$-regularity theory for parabolic equations with integro-differential operators having low intensity kernels
by: Kang, Jaehoon, et al.
Published: (2023)

The bilateral generalized inverse Gaussian process with applications to financial modeling
by: Agazzotti, Gaetano, et al.
Published: (2024)

Uniqueness in law for singular degenerate SDEs with respect to a (sub-)invariant measure
by: Lee, Haesung, et al.
Published: (2024)

Stochastic Calculus for Rough Fractional Brownian Motion via Operator Factorization
by: Fontes, Ramiro
Published: (2026)

$L^p$-$L^q$ estimates for transition semigroups associated to dissipative stochastic systems
by: Angiuli, Luciana, et al.
Published: (2023)

Regularisation of cylindrical Lévy processes in Besov spaces
by: Griffiths, Matthew, et al.
Published: (2024)

Nonlinear Dirichlet problem of non-local branching processes
by: Beznea, Lucian, et al.
Published: (2024)

A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval
by: Bobrowski, Adam, et al.
Published: (2025)

On generators of transition semigroups associated to semilinear stochastic partial differential equations
by: Bignamini, D. A., et al.
Published: (2020)

High-contrast periodic random jumps in continuum and limit Markov process
by: Piatnitski, Andrey, et al.
Published: (2024)

Law equivalence for Ornstein--Uhlenbeck dynamics driven by Lévy noise
by: Kania, Tomasz
Published: (2025)

Nonlinear semigroups and limit theorems for convex expectations
by: Blessing, Jonas, et al.
Published: (2022)

Schauder regularity results in separable Hilbert spaces
by: Bignamini, Davide A., et al.
Published: (2022)

A tree-like fractal Dirichlet space lying between strong and weak elliptic Harnack inequalities
by: Huang, Caoxu, et al.
Published: (2026)

Around the Sobolev Inequalities for the Stable Heat Semigroups
by: Arras, Benjamin, et al.
Published: (2025)

On the Cauchy problem for non-local Ornstein--Uhlenbeck operators
by: Priola, Enrico, et al.
Published: (2015)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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