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Related papers: Schr\"odinger's problem with constraints

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We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…

Spectral Theory · Mathematics 2025-05-13 Alexander Mikhaylov , Victor Mikhaylov

This paper deals with optimal prediction in a regime-switching model driven by a continuous-time Markov chain. We extend existing results for geometric Brownian motion by deriving optimal stopping strategies that depend on the current…

Probability · Mathematics 2016-06-27 Yue Liu , Nicolas Privault

The final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the…

Dynamical Systems · Mathematics 2020-09-01 Graziano Crasta , Alessio Falocchi , Filippo Gazzola

This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…

Probability · Mathematics 2019-11-19 Simone Di Marino , Augusto Gerolin

We derive new limit theorems for Brownian motion, which can be seen as non-exponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits…

Probability · Mathematics 2018-10-05 Julio Backhoff-Veraguas , Daniel Lacker , Ludovic Tangpi

We consider a directed random walk making either 0 or $+1$ moves and a Brownian bridge, independent of the walk, conditioned to arrive at point $b$ on time $T$. The Hamiltonian is defined as the sum of the square of increments of the bridge…

Condensed Matter · Physics 2016-08-31 Servet Martinez , Dimitri Petritis

We propose a procedure for estimating the Schr\"odinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks…

Machine Learning · Statistics 2024-08-22 Aram-Alexandre Pooladian , Jonathan Niles-Weed

We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…

Probability · Mathematics 2020-02-04 Jean-Dominique Deuschel , Henri Elad Altman , Tal Orenshtein

Numerical solutions of the time-dependent Schr\"odinger equation based on the variational principle may offer physical insight that cannot be gained by a solution using fixed grids in position and momentum space. Here we focus on the…

Quantum Physics · Physics 2024-02-22 Frank Grossmann

In this paper, we introduce an extension of a Brownian bridge with a random length by including uncertainty also in the pinning level of the bridge. The main result of this work is that unlike for deterministic pinning point, the bridge…

Probability · Mathematics 2021-12-22 Mohammed Louriki

We derive closed-form solutions to the optimal stopping problems related to the pricing of perpetual American standard and lookback put and call options in the extensions of the Black-Merton-Scholes model with progressively enlarged…

Mathematical Finance · Quantitative Finance 2025-07-08 Pavel V. Gapeev , Libo Li

Kyle (1985) builds a pioneering and influential model, in which an insider with long-lived private information submits an optimal order in each period given the market maker's pricing rule. An inconsistency exists to some extent in the…

Trading and Market Microstructure · Quantitative Finance 2010-12-13 Fuzhou Gong , Deqing Zhou

Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…

Machine Learning · Statistics 2024-04-23 Jhanvi Garg , Xianyang Zhang , Quan Zhou

The Entropic Optimal Transport (EOT) problem and its dynamic counterpart, the Schr\"odinger bridge (SB) problem, play an important role in modern machine learning, linking generative modeling with optimal transport theory. While recent…

For the classical principal chiral model with boundary, we give the subset of the Yangian charges which remains conserved under certain integrable boundary conditions, and extract them from the monodromy matrix. Quantized versions of these…

High Energy Physics - Theory · Physics 2009-11-07 G. W. Delius , N. J. MacKay , B. J. Short

In this paper, we explore cooperative and competitive coupled obstacle systems, which, up to now, are new type obstacle systems and formed by coupling two equations belonging to classical obstacle problem. On one hand, applying the…

Analysis of PDEs · Mathematics 2024-09-16 Lili Du , Xu Tang , Cong Wang

We provide a solution to the problem of optimal transport by Brownian martingales in general dimensions whenever the transport cost satisfies certain subharmonic properties in the target variable, as well as a stochastic version of the…

Analysis of PDEs · Mathematics 2020-10-07 Nassif Ghoussoub , Young-Heon Kim , Aaron Zeff Palmer

In this paper, we consider the large deviations for dynamical Schr\"odinger problems, using the variational approach developed by Dupuis, Ellis, Budhiraja, and others. Recent results on scaled families of Schr\"odinger problems, in…

Probability · Mathematics 2025-11-21 Viktor Nilsson , Pierre Nyquist

The analogies between economics and classical mechanics can be extended from constrained optimization to constrained dynamics by formalizing economic (constraint) forces and economic power in analogy to physical (constraint) forces in…

Theoretical Economics · Economics 2021-06-28 Oliver Richters

In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we…

Statistical Mechanics · Physics 2017-10-11 Alain Mazzolo