Derivation of a stochastic maximum principle for McKean-Vlasov SDEs with common noise that requires a third adjoint state to linearize all second-order terms in the cost expansion.
Sznitman,Topics in propagation of chaos, in École d’Été de Probabilités de Saint-Flour XIX—1989, vol
6 Pith papers cite this work. Polarity classification is still indexing.
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Attention in minimal transformers under corruption performs in-context empirical Bayes via a single kernel-weighted posterior mean step followed by depth-driven particle dynamics refinement.
Maximum entropy inference on weight distributions under context-dependent task constraints produces neuron populations with contextual gain modulation whose connectivity matches gradient-descent trained networks, with transitions to random structure as context count or weight scale increases.
Neural surrogates enable a four-stage alternating algorithm for nonlocal mean-field Schrödinger bridges with linear scaling and Gronwall stability bounds.
Proves existence of self-intersection local times and a change-of-variable formula for Volterra Gaussian processes inside stochastic flows with interaction, plus asymptotics and results for unbounded weights.
Establishes a comparison principle for two-population killed-particle HJB equations on decomposed state spaces of alive measures and cemetery masses, plus mean-field limit and particle convergence results.
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Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise
Derivation of a stochastic maximum principle for McKean-Vlasov SDEs with common noise that requires a third adjoint state to linearize all second-order terms in the cost expansion.
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Attention as In-Context Empirical Bayes: A Two-Stage View via Particle Dynamics
Attention in minimal transformers under corruption performs in-context empirical Bayes via a single kernel-weighted posterior mean step followed by depth-driven particle dynamics refinement.
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Balancing structure and randomness: maximum entropy networks for context-dependent computations
Maximum entropy inference on weight distributions under context-dependent task constraints produces neuron populations with contextual gain modulation whose connectivity matches gradient-descent trained networks, with transitions to random structure as context count or weight scale increases.
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Nonlocal Mean Field Schr\"{o}dinger Bridge with Learned Interactions
Neural surrogates enable a four-stage alternating algorithm for nonlocal mean-field Schrödinger bridges with linear scaling and Gronwall stability bounds.
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Self-intersection local times for Volterra Gaussian processes in stochastic flows with interaction
Proves existence of self-intersection local times and a change-of-variable formula for Volterra Gaussian processes inside stochastic flows with interaction, plus asymptotics and results for unbounded weights.
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Controlled McKean--Vlasov Contagion with State-Dependent Killing
Establishes a comparison principle for two-population killed-particle HJB equations on decomposed state spaces of alive measures and cemetery masses, plus mean-field limit and particle convergence results.