Related papers: Projective stochastic equations and nonlinear long…
We consider a nonlinear filtering problem for a signal-observation system driven by a Volterra-type Gaussian rough path, whose sample paths may exhibit greater roughness than those of Brownian motion. The observation process includes a…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
In this paper, we develop a new general approach to the existence and uniqueness theory of infinite dimensional stochastic equations of the form dX+A(t)Xdt = XdW in (0;T)xH, where A(t) is a nonlinear monotone and demicontinuous operator…
Multivariate dynamic time series models are widely encountered in practical studies, e.g., modelling policy transmission mechanism and measuring connectedness between economic agents. To better capture the dynamics, this paper proposes a…
Projective Simulation was introduced as a novel approach to Artificial Intelligence. It involves a deliberation procedure that consists of a random walk on a graph of clips and allows for the learning agent to project itself into the future…
By modeling the interaction of an open quantum system with its environment through a natural generalization of the classical concept of continuous time random walk, we derive and characterize a class of non-Markovian master equations whose…
Most existing vision-language-action (VLA) models for robotic manipulation lack progress awareness, typically relying on hand-crafted heuristics for task termination. This limitation is particularly severe in long-horizon tasks involving…
In this paper we study several classes of stochastic optimization algorithms enriched with heavy ball momentum. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic dual…
We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
Molecular simulations of many particles which move rather according to a brownian than a newtonian type of dynamics, nevertheless, can be performed by means of a "velocity-Verlet-like" algorithm. The derivation of this algorithm requires…
We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing can be notably applied to incremental first-order methods such as the stochastic…
Natural spatiotemporal processes can be highly non-stationary in many ways, e.g. the low-level non-stationarity such as spatial correlations or temporal dependencies of local pixel values; and the high-level variations such as the…
We develop a data-driven framework for identifying non-Markovian dynamical equations of motion for open quantum systems. Starting from the Nakajima--Zwanzig formalism, we vectorize the reduced density matrix into a four-dimensional state…
We introduce a local non-determinism condition for Volterra It\^{o} processes that captures smoothing properties of possibly degenerate noise. By combining the stochastic sewing lemma with one-step Euler approximations, we first prove the…
We introduce an alternative to the notion of `fast rate' in Learning Theory, which coincides with the optimal error rate when the given class happens to be convex and regular in some sense. While it is well known that such a rate cannot…
We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pathwise uniqueness of a non-negative c\`adl\`ag solution. By…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
Long-run covariance matrix estimation is the building block of time series inference. The corresponding difference-based estimator, which avoids detrending, has attracted considerable interest due to its robustness to both smooth and abrupt…