Related papers: Convergence of an Adaptive Approximation Scheme fo…
In this paper we propose a new deterministic approximation method, called discretization approximation, for Bayesian computation. Discretization approximation is very simple to understand and to implement, It only requires calculating…
The maximum entropy principle is a powerful tool for solving underdetermined inverse problems. This paper considers the problem of discretizing a continuous distribution, which arises in various applied fields. We obtain the approximating…
The inverse first-passage time problem determines a boundary such that the first-passage time of a Wiener process to this boundary has a given distribution. An approximation which is based on the starting value of the boundary to a smooth…
It is common practice to treat small jumps of L\'evy processes as Wiener noise and thus to approximate its marginals by a Gaussian distribution. However, results that allow to quantify the goodness of this approximation according to a given…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
A discretization scheme for nonnegative diffusion processes is proposed and the convergence of the corresponding sequence of approximate processes is proved using the martingale problem framework. Motivations for this scheme come typically…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
The distance between the true and numerical solutions in some metric is considered as the discretization error magnitude. If error magnitude ranging is known, the triangle inequality enables the estimation of the vicinity of the approximate…
We consider a problem of replication of random vectors by ordinary integrals in the setting when a underlying random variable is generated by a Wiener process. The goal is to find an optimal adapted process such that its cumulative integral…
We study the weak approximation error of a skew diffusion with bounded measurable drift and H\"older diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first…
In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…
In this paper we deal with global approximation of solutions of stochastic differential equations (SDEs) driven by countably dimensional Wiener process. Under certain regularity conditions imposed on the coefficients, we show lower bounds…
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
The Euler scheme is a standard time discretization for BSDEs, but its implementation hinges on approximating conditional expectations and the associated martingale terms at each time step. We propose an implementation based on the Wiener…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…
We study a triple of stochastic processes: a Wiener process $W_t$, $t \geq 0$, its running maxima process $M_t=\sup \{W_s: s \in [0,t]\}$ and its running minima process $m_t=\inf \{W_s: s \in [0,t]\}$. We derive the analytical formulas for…
We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…