Related papers: Stochastic functional differential equations and s…
Several versions of It\^{o}'s formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of…
We investigate the dynamics of kinetically constrained models of glass formers by analysing the statistics of trajectories of the dynamics, or histories, using large deviation function methods. We show that, in general, these models exhibit…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
We study a stochastic model of protein dynamics that explicitly includes delay in the degradation. We rigorously derive the master equation for the processes and solve it exactly. We show that the equations for the mean values obtained…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…
Stochastic memoization is a higher-order construct of probabilistic programming languages that is key in Bayesian nonparametrics, a modular approach that allows us to extend models beyond their parametric limitations and compose them in an…
Researchers rely on the distance function to model multiple product production using multiple inputs. A stochastic directional distance function (SDDF) allows for noise in potentially all input and output variables. Yet, when estimated, the…
It is shown that under a certain condition on a semimartingale and a time-change, any stochastic integral driven by the time-changed semimartingale is a time-changed stochastic integral driven by the original semimartingale. As a direct…
Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…
Expanding on neural operators, we propose a novel framework for stochastic process learning across arbitrary domains. In particular, we develop operator flow matching (OFM) for learning stochastic process priors on function spaces. OFM…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
Fractional order differential and difference equations are used to model systems with memory. Variable order fractional equations are proposed to model systems where the memory changes in time. We investigate stability conditions for linear…
This paper is devoted to a stochastic differential game of functional forward-backward stochastic differential equation (FBSDE, for short). The associated upper and lower value functions of the stochastic differential game are defined by…
Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what…
Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…