Related papers: A Formalization of Martingales in Isabelle/HOL
We present the formalization of Doob's martingale convergence theorems in the mathlib library for the Lean theorem prover. These theorems give conditions under which (sub)martingales converge, almost everywhere or in $L^1$. In order to…
We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued…
We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…
Formal programming language semantics are imperative when trying to verify properties of programs in an automated manner. Using a new approach, Din et al. strengthen the ability of reasoning about concurrent programs by proposing a modular…
We observe a multilinearity preserving property of conditional expectation for infinite dimensional independent increment processes defined on some abstract Banach space $B$. It is similar in nature to the polynomial preserving property…
Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we…
When analyzing probabilistic computations, a powerful approach is to first find a martingale---an expression on the program variables whose expectation remains invariant---and then apply the optional stopping theorem in order to infer…
For a real Borel measurable function b, which satisfies certain integrability conditions, it is possible to define a stochastic integral of the process b(Y) with respect to a Brownian motion W, where Y is a diffusion driven by W. It is well…
In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…
An estimation method is proposed for a wide variety of discrete time stochastic processes that have an intractable likelihood function but are otherwise conveniently specified by an integral transform such as the characteristic function,…
The formalisation of mathematics is continuing rapidly, however combinatorics continues to present challenges to formalisation efforts, such as its reliance on techniques from a wide range of other fields in mathematics. This paper presents…
We consider decoupling inequalities for random variables taking values in a Banach space $X$. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be…
In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norming in the spirit of the classical Law of Iterated Logarithm. Key words: Martingales, exponential estimations,…
Supermartingales are here defined on a non-probabilistic setting and can be interpreted solely in terms of superhedging operations. The classical expectation operator is replaced by a pair of subadditive operators one of them providing a…
Using a multiplicative structure (for example that of a Banach algebra) and a partial order we construct a weak version of a Banach space valued stochastic integral with respect to square integrable martingales.
Many results in stochastic analysis and mathematical finance involve local martingales. However, specific examples of strict local martingales are rare and analytically often rather unhandy. We study local martingales that follow a given…
A Neural Process (NP) estimates a stochastic process implicitly defined with neural networks given a stream of data, rather than pre-specifying priors already known, such as Gaussian processes. An ideal NP would learn everything from data…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
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…