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On the area swept by a biased diffusion till its first-exit time: martingale approach and gambling opportunities
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with...
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Martingale Structure for General Thermodynamic Functionals of Diffusion Processes Under Second-Order Averaging
Novel hidden thermodynamic structures have recently been uncovered during the investigation of nonequilibrium thermodynamics for multiscale...
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Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
We prove the existence of non-negative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in...
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On Weak-Strong Uniqueness for Stochastic Equations of Incompressible Fluid Flow
We introduce a concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid...
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Global Existence of Martingale Solutions and Large Time Behavior for a 3D Stochastic Nonlocal Cahn–Hilliard–Navier–Stokes Systems with Shear Dependent Viscosity
In this paper, we consider a stochastic version of a nonlinear system which consists of the incompressible Navier–Stokes equations with shear...
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Gaussian Fluctuations for Interacting Particle Systems with Singular Kernels
We consider the asymptotic behaviour of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove...
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Sticky Brownian Motions and a Probabilistic Solution to a Two-Point Boundary Value Problem
In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval (0,1) with boundary conditions which...
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Black-Scholes-Differentialgleichung
Nachdem die Black-Scholes-Gleichung für eine Call-Option aus der Anforderung abgeleitet wurde, ein Portfolio risikofrei zu gestalten, wird die...
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Stochastic Landau–Lifshitz–Bloch Equation with Transport Noise: Well-Posedness, Dissipation Enhancement
The Landau–Lifshitz–Bloch equation is the only valid model describing the simulation of heat-assisted magnetic recording around the Curie...
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A Consistent Stochastic Large-Scale Representation of the Navier–Stokes Equations
In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier–Stokes equations defined in the...
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Dissipative Solutions to the Stochastic Euler Equations
We study the three-dimensional incompressible Euler equations subject to stochastic forcing. We develop a concept of dissipative martingale...
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John–Nirenberg Inequalities for Noncommutative Column BMO and Lipschitz Martingales
In this paper, we continue the study of John–Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. As conjectured...
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Concentration Inequalities for Output Statistics of Quantum Markov Processes
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for...
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Derivation of Coupled KPZ Equations from Interacting Diffusions Driven by a Single-Site Potential
The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is derived from various microscopic models, and to...
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New Characterization of the Weak Disorder Phase of Directed Polymers in Bounded Random Environments
We show that the weak disorder phase for the directed polymer model in a random environment is characterized by the integrability of the running...
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The High-Order Corrections of Discrete Harmonic Measures and Their Correction Constants
By the dimension reduction idea, overshoot for random walks, coupling and martingale arguments, we obtain a simpler and easily computable expression...
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M-Diagrams
This chapter suggests that Martingale, or M-Diagrams, can be used as a simple method for comparing clocks. M-Diagrams allow for clock comparison by...