Related papers: Computable Stochastic Processes
We present a novel approach for explaining Gaussian processes (GPs) that can utilize the full analytical covariance structure present in GPs. Our method is based on the popular solution concept of Shapley values extended to stochastic…
We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a…
We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
In this paper, we introduce a foundation for computable model theory of rational Pavelka logic (an extension of {\L}ukasiewicz logic) and continuous logic, and prove effective versions of some theorems in model theory. We show how to reduce…
In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density…
We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…
We consider trawl processes, which are stationary and infinitely divisible stochastic processes and can describe a wide range of statistical properties, such as heavy tails and long memory. In this paper, we develop the first…
We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These…
Renewable energy projects, such as large offshore wind farms, are critical to achieving low-emission targets set by governments. Stochastic computer models allow us to explore future scenarios to aid decision making whilst considering the…
This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are…
Over the last decade, a series of applied mathematics papers have explored a type of inverse problem--called by a variety of names including "inverse sensitivity", "pushforward based inference", "consistent Bayesian inference", or…