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Null events and stochastical independence

Giulianella Colleti, Romano Scozzafava (1998)

Kybernetika

In this paper we point out the lack of the classical definitions of stochastical independence (particularly with respect to events of 0 and 1 probability) and then we propose a definition that agrees with all the classical ones when the probabilities of the relevant events are both different from 0 and 1, but that is able to focus the actual stochastical independence also in these extreme cases. Therefore this definition avoids inconsistencies such as the possibility that an event A can be at the...

Number of hidden states and memory: a joint order estimation problem for Markov chains with Markov regime

Antoine Chambaz, Catherine Matias (2009)

ESAIM: Probability and Statistics

This paper deals with order identification for Markov chains with Markov regime (MCMR) in the context of finite alphabets. We define the joint order of a MCMR process in terms of the number k of states of the hidden Markov chain and the memory m of the conditional Markov chain. We study the properties of penalized maximum likelihood estimators for the unknown order (k, m) of an observed MCMR process, relying on information theoretic arguments. The novelty of our work relies in the joint...

Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations***

Shige Peng, Mingyu Xu (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations***

Shige Peng, Mingyu Xu (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Numerical analysis of parallel replica dynamics

Gideon Simpson, Mitchell Luskin (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Parallel replica dynamics is a method for accelerating the computation of processes characterized by a sequence of infrequent events. In this work, the processes are governed by the overdamped Langevin equation. Such processes spend much of their time about the minima of the underlying potential, occasionally transitioning into different basins of attraction. The essential idea of parallel replica dynamics is that the exit distribution from a given well for a single process can be approximated by...

Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

Antoine Gloria (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice ℤ d with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...

Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

Antoine Gloria (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice ℤ d with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...

Numerical schemes for multivalued backward stochastic differential systems

Lucian Maticiuc, Eduard Rotenstein (2012)

Open Mathematics

We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: d Y t + F ( t , X t , Y t , Z t ) d t ∈ ∂ φ ( Y t ) d t + Z t d W t , where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational...

Numerical solution of a stochastic model of a ball-type vibration absorber

Fischer, Cyril, Náprstek, Jiří (2021)

Programs and Algorithms of Numerical Mathematics

The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can...

Numerical solution of Black-Scholes option pricing with variable yield discrete dividend payment

Rafael Company, Lucas Jódar, Enrique Ponsoda (2008)

Banach Center Publications

This paper deals with the construction of numerical solution of the Black-Scholes (B-S) type equation modeling option pricing with variable yield discrete dividend payment at time t d . Firstly the shifted delta generalized function δ ( t - t d ) appearing in the B-S equation is approximated by an appropriate sequence of nice ordinary functions. Then a semidiscretization technique applied on the underlying asset is used to construct a numerical solution. The limit of this numerical solution is independent of the...

Numerical solutions of the mass transfer problem

Serge Dubuc, Issa Kagabo (2006)

RAIRO - Operations Research

Let μ and ν be two probability measures on the real line and let c be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure ξ whose marginals coincide with μ and ν, and whose total cost ∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval. We illustrate these numerical...

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