271 papers
This paper empirically demonstrates that while the runtime of local greedy search for optimizing Sherrington-Kirkpatrick spin glass Hamiltonians is universal across various coupling distributions, the performance of Parisi's local reluctant search is surprisingly non-universal and sensitive to the specific entry distribution, particularly when couplings have discrete support.
This paper introduces a canonical framework for jointly lifting Brownian motion and low-regularity stochastic rough paths to model rough volatility via a single rough differential equation, thereby extending existing partial rough path theories, providing a numerical approximation scheme for correlated settings, and demonstrating successful calibration to market data.
This paper introduces and proves the convergence of a Martingale Sinkhorn algorithm in arbitrary dimensions for solving the martingale Benamou–Brenier optimal transport problem, extending the theory to marginals with finite moments of order without requiring compact support.
This paper introduces efficient, parameter-free geodesic slice sampling algorithms for generating samples from probability distributions on the sphere, proving their uniform ergodicity and demonstrating superior performance over standard methods like random-walk Metropolis-Hastings and Hamiltonian Monte Carlo in challenging directional data scenarios.
This paper investigates the distributional and asymptotic properties of the supremum and infimum of Brownian motion with drift and exponential resetting, deriving explicit renewal formulas, survival function approximations, and new expressions for the finite-dimensional distributions in the stationary case.
This paper solves an intertemporal utility maximization problem with a no-borrowing constraint and stochastic excess returns in the Kim-Omberg framework by employing Lagrange duality to transform the primal problem into a dual singular control problem, which is then characterized via an auxiliary two-dimensional optimal stopping problem to derive optimal consumption and portfolio strategies.
This paper investigates the asymptotic behaviors of randomly weighted sums with upper tail asymptotically independent increments under new conditions without requiring moment assumptions on the weights, deriving uniform asymptotics and applying them to estimate finite-time ruin probabilities in discrete-time risk models.
This paper establishes a combinatorial proof that the basin walls of coalescing particles on a line form a Pfaffian point process for any skip-free dynamics, deriving exact correlation formulas, proving a central limit theorem via indecomposability, and identifying a checkerboard duality between these walls and the surviving particles of a dual process.
This paper introduces a general determinantal framework for analyzing coalescing random walks on a line, providing exact finite-dimensional distributions for survivor systems and deriving known results like the Rayleigh spacing density and joint gap distributions through a unified method applicable to arbitrary nearest-neighbor walks and their Brownian limits.
This paper establishes the existence and uniqueness of solutions to G-SVIEs under time-varying and integral-Lipschitz conditions using Picard iteration, while also proving the continuity of solutions with respect to parameters in the Lipschitz case.
This paper introduces a ghost particle method to derive exact determinantal and Pfaffian formulas for computing annihilation probabilities in particle systems, effectively overcoming the challenge of variable particle counts by treating annihilated particles as invisible walkers and extending these results to coalescence and various stochastic processes.
This paper introduces a "ghost particle" method that preserves the total particle count during coalescence events, thereby enabling the derivation of exact determinant formulas for arbitrary coalescence patterns in Markovian particle systems ranging from discrete lattices to continuous diffusions.
This paper establishes a hydrodynamic limit for a multiscale stochastic compartmental model of hematopoiesis, proving that the dynamics of stem, immature, and mature cells converge to a deterministic system of partial differential equations with boundary conditions as the number of immature compartments approaches infinity.
This paper derives a new closed-form formula for the characteristic function of the asymmetric Student's -distribution by establishing a novel integral representation involving the sine function and the exponential integral, which subsequently yields a closed-form expression for a specific limit involving modified Bessel and Struve functions.
This paper investigates multidimensional elephant random walks with stops and random step sizes, establishing key convergence results such as the law of large numbers, the law of the iterated logarithm, and the central limit theorem for the number of moves using martingale methods.
This paper establishes the existence and uniqueness of solutions to backward stochastic differential equations driven by G-Brownian motion under time-varying monotonicity and Lipschitz conditions by utilizing the Yosida approximation method.
This paper establishes the global well-posedness and long-time behavior of stochastic forced 3D Navier-Stokes equations in the critical -space by leveraging the regularization effect of transport and nonlocal turbulent noise through Lyapunov functions, bootstrap estimates, and stopping time arguments.
This paper establishes that a discrete-time stochastic clustering model on , where points move halfway toward randomly chosen neighbors and merge, converges to a unique weak limit with exponential gap tails when initialized as a renewal process, and further characterizes the scaling limit of its time-reversed dynamics as a random distribution function.
This paper establishes new sufficient conditions for the non-explosivity and positive recurrence of stochastic reaction networks within compartments whose fragmentation rates depend on their internal species content, demonstrating that previous theoretical results for content-independent dynamics fail in this more general, biologically relevant setting.
This paper establishes a strong approximation scheme for stochastic differential and Volterra equations with merely measurable or singular time-dependent coefficients by replacing the Brownian motion with a compound Poisson process, proving explicit convergence rates and demonstrating superior stability compared to traditional Euler-Maruyama methods.