A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
Framework infers Langevin dynamics from stochastic observations of latent systems.
Study on fake stationary Volterra Heston model for non-stationary processes.
New method optimizes SDE models using continuous-time gradient descent.
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show that SGD with constant rates can be effectively used as an approximate posterio…
This work introduces a new model for complex stochastic processes.
Study optimal transport for stationary processes, estimating joinings and costs.
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a u…
ConvNP improves SP prediction with translation equivariance and coherent samples.
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotically consistent algorithms is designed for clustering offline and online datasets, respectively. We also suggest a formal criterion on the eff…
Proposes a new method combining Reservoir Computing and Normalizing Flow for predicting stochastic dynamical systems.
The paper studies convergence of kernel autocovariance operators for stationary processes.
SAMoSSA combines mSSA and AR for accurate time series analysis.
The paper extends NSGPs with -regularization for sparsity and solves the resulting R-NSGP regression problem.
The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with non-stationary process…
Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…
Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes. However, a large class of problems comprises underlying temporal dependency structures in a sequence of stochastic processes that Neural Processes (NP) do not e…
Noise balance theory explains SGD's behavior in neural networks.
ETGP improves multi-class classification efficiency.
Estimates stationary distribution from batch transitions without access to the underlying process.
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this cla…
This note develops a stochastic model of asset volatility. The volatility obeys a continuous-time autoregressive equation. Conditions under which the process is asymptotically stationary and possesses long memory are characterised. Connections with the class of ARCH() processes are sketched.
The state of a stochastic process evolving over a time is typically assumed to lie on a normal distribution whose width scales like . However, processes where the probability distribution is not normal and the scaling exponent differs from are known. The search for possible origins of such "a…
Exact results on power-law distributions in systems with resets.
Estimates stationary mass and frequency from non-i.i.d. data.
Developing a climate-aware pricing framework for XL reinsurance and CAT bonds under non-stationary catastrophe risk.
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
A new kernel improves Gaussian process performance for non-stationary data.
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
We build a sequence of empirical measures on the space D(R_+,R^d) of R^d-valued càdlàg functions on R_+ in order to approximate the law of a stationary R^d-valued Markov and Feller process (X_t). We obtain some general results of convergence of this sequence. Then, we apply them to Brownian diffusions and solutions to …
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and non-uniformly smooth spatial boundaries. A Gaussian process regression using a non-stat…
In this work, we propose a new Gaussian process regression (GPR) method: physics information aided Kriging (PhIK). In the standard data-driven Kriging, the unknown function of interest is usually treated as a Gaussian process with assumed stationary covariance with hyperparameters estimated from data. In PhIK, we compu…
A survey is performed of various Multi-Armed Bandit (MAB) strategies in order to examine their performance in circumstances exhibiting non-stationary stochastic reward functions in conjunction with delayed feedback. We run several MAB simulations to simulate an online eCommerce platform for grocery pick up, optimizing …
We present a novel variation of online kernel machines in which we exploit a consensus based optimization mechanism to guide the evolution of decision functions drawn from a reproducing kernel Hilbert space, which efficiently models the observed stationary process.
New method reduces computational cost for learning stationary diffusions.
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on stationary problems, and permitting learning rates to grow appropriately in non-stati…
New algorithms improve GP inference without approximations, achieving better results.
Paper uses RL for market making, improving stability in non-stationary markets.
Estimates network structure from correlated node outputs of wide-sense stationary processes.
In this paper, we develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market or…
Study reveals convergence properties of SGD with random learning rate.
The concept of SCN offers a fast framework with universal approximation guarantee for lifelong learning of non-stationary data streams. Its adaptive scope selection property enables for proper random generation of hidden unit parameters advancing conventional randomized approaches constrained with a fixed scope of rand…
The paper tackles finding stationary points in stochastic convex optimization problems.
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust …
Reinforcement learning algorithms rely on exploration to discover new behaviors, which is typically achieved by following a stochastic policy. In continuous control tasks, policies with a Gaussian distribution have been widely adopted. Gaussian exploration however does not result in smooth trajectories that generally c…