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Averaging Principle for Two Time-Scales Stochastic Partial Differential Equations with Reflection
In this work, we consider a system of fast and slow time-scale stochastic partial differential equations with reflection, where the slow component is...
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Strong Averaging Principle for Slow–Fast Stochastic Partial Differential Equations with Locally Monotone Coefficients
This paper is devoted to proving the strong averaging principle for slow–fast stochastic partial differential equations with locally monotone...
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General Coupled Mean-Field Reflected Forward-Backward Stochastic Differential Equations
In this paper we consider general coupled mean-field reflected forward-backward stochastic differential equations (FBSDEs), whose coefficients not...
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Linear Quadratic Optimal Control for Systems Governed by First-Order Hyperbolic Partial Differential Equations
This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations...
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Approximate Controllability of a Coupled Nonlocal Partial Functional Integro-differential Equations with Impulsive Effects
In this work, we study the approximate controllability problem for a system of nonlocal integro-differential equations with impulsive effects. We...
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A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks
In this paper, physics-informed liquid networks (PILNs) are proposed based on liquid time-constant networks (LTC) for solving nonlinear partial...
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Physics Informed Cellular Neural Networks for Solving Partial Differential Equations
Physics-Informed Neural Networks (PINNs) are a scientific machine learning technique used to solve a broad class of problems. PINNs approximate...
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A Short Note on Solving Partial Differential Equations Using Convolutional Neural Networks
Solving partial differential equations (PDEs) is a common task in numerical mathematics and scientific computing. Typical discretization schemes, for...
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Nash Equilibria Strategies and Equivalent Single-Objective Optimization Problems. The Case of Linear Partial Differential Equations
In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach...
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Fully coupled drift-less forward and backward stochastic differential equations in a degenerate case
Existence and uniqueness results of fully coupled forward stochastic differential equations without drifts and backward stochastic differential...
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A Low-Rank Solver for Parameter Estimation and Uncertainty Quantification in Time-Dependent Systems of Partial Differential Equations
In this work we propose a low-rank solver in view of performing parameter estimation and uncertainty quantification in systems of partial...
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A Strong Averaging Principle Rate for Two-Time-Scale Coupled Forward–Backward Stochastic Differential Equations Driven by Fractional Brownian Motion
This paper concerns the strong convergence rate of an averaging principle for two-time-scale coupled forward–backward stochastic differential...
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Stackelberg Stochastic Differential Games in Feedback Information Pattern with Applications
This paper is concerned with both nonzero-sum and zero-sum Stackelberg stochastic differential games on a finite horizon in feedback information...
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Coupled McKean–Vlasov Equations Over Convex Domains
In this paper, the reflected McKean–Vlasov diffusion ov a convex domain is studied. We first establish the well-posedness of a coupled system of...
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Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications
We study a general kind of partial information nonzero sum two-player stochastic differential games, where the state variable is governed by a...
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Backward Linear-Quadratic Mean Field Social Optima with Partial Information
This paper is concerned with the linear-quadratic social optima for a class of N weakly coupled backward system with partial information structure....
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Stochastic differential games with controlled regime-switching
In this article, we consider a two-player zero-sum stochastic differential game with regime-switching. Different from the results in existing...
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Lp-Estimate for Linear Forward-Backward Stochastic Differential Equations
This paper is concerned with coupled linear forward-backward stochastic differential equations (FBSDEs, for short). When the homogeneous coefficients...
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Stochastic Variational Principles for Dissipative Equations with Advected Quantities
This paper presents symmetry reduction for material stochastic Lagrangian systems with advected quantities whose configuration space is a Lie group....