相关论文: Choquet expectations and g-expectations with multi…

Chandrasekhar's theory of stellar encounters predicts a dependence of the Brownian motion of a massive particle on the velocity distribution of the perturbing stars. One consequence is that the expectation value of the massive object's…

For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis,…

We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is…

Consideration of some perturbatively calculated gauge-invariant expectation values of local noncomposite operators in pure Yang-Mills theory indicates that those expectation values which are not dimension specific, and which are well…

We establish Harnack inequality and shift Harnack inequality for stochastic differential equation driven by $G$-Brownian motion. As applications, the uniqueness of invariant linear expectations and estimates on the $\sup$-kernel are…

This paper investigates the strict comparison theorem under the framework of $G$-expectation, i.e., let $X\leq Y$ q.s., if $X,Y$ satisfy some additional conditions, then $\E[X]<\E[Y]$.

In this article, we follow the study of quadratic backward SDEs with jumps,that is to say for which the generator has quadratic growth in the variables (z; u), started in our accompanying paper [15]. Relying on the existence and uniqueness…

By using the Picard iteration scheme, this article establishes the existence and uniqueness theory for solutions to stochastic functional differential equations driven by G-Browniain motion. Assuming the monotonicity conditions, the…

A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…

Let $B_s$ be a three dimensional Brownian motion and $\omega(dx)$ be an independent Poisson field on $\mathbb{R}^3$. It is proved that for any $t>0$, conditionally on $\omega(\cdot)$, \label{*} \mathbb{E}_0 \exp\{\theta \int_0^t…

A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…

An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…

In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional, such as the mean or a quantile of the predictive distribution. When evaluating and comparing competing…

From a given nuclear triplet we construct a nuclear triplet of sequence spaces and introduce a correlated Gaussian measure via the Bochner-Minlos theorem. Considering special types of correlation operators on such sequence spaces, certain…

We consider the well-posedness problem of multi-dimensional reflected backward stochastic differential equations driven by $G$-Brownian motion ($G$-BSDEs) with diagonal generators. Two methods, i.e., the penalization method and the Picard…

We consider two bivariate models with two-way interactions in context of risk and queueing theory. The two entities interact with each other by providing assistance but otherwise evolve independently. We focus on certain random quantities…

We explore a background-independent theory of composite gravity. The vacuum expectation value of the composite metric satisfies Einstein's equations (with corrections) as a consistency condition, and selects the vacuum spacetime. A…

We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of…

We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the…