The Experts below are selected from a list of 7317 Experts worldwide ranked by ideXlab platform
Mariusz Nieweglowski - One of the best experts on this subject based on the ideXlab platform.
-
semimartingales and shrinkage of filtration
Annals of Applied Probability, 2021Co-Authors: Tomasz R Bielecki, Monique Jeanblanc, Jacek Jakubowski, Mariusz NieweglowskiAbstract:We consider a Complete Probability Space (Ω,F,P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F⊂G. On this Probability Space we consider a real valued G-semimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compute the F-semimartingale characteristics of the F-optional projection of X in terms of the G-canonical decomposition and the G-semimartingale characteristics of X. In this paper problem B is solved under the assumption that the filtration F is immersed in G. Beyond the obvious mathematical interest, our study is motivated by important practical applications in areas such as finance and insurance (cf. Structured Dependence Between Stochastic Processes (2020) Cambridge Univ. Press).
Jornet Sanz Marc - One of the best experts on this subject based on the ideXlab platform.
-
Mathematical methods for the randomized non-autonomous Bertalanffy model
Texas State University, 2020Co-Authors: Calatayud Gregori Julia, Caraballo Garrido Tomás, Cortés López, Juan Carlos, Jornet Sanz MarcAbstract:In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, x(t0, ω) = x0(ω), where a(t, ω) and b(t, ω) are stochastic processes and x0(ω) is a random variable, all of them defined in an underlying Complete Probability Space. Under certain assumptions on a, b and x0, we obtain a solution stochastic process, x(t, ω), both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loève expansions, we construct a sequence of Probability density functions that under certain conditions converge pointwise or uniformly to the density function of x(t, ω), fx(t) (x). This permits approximating the expectation and the variance of x(t, ω). At the end, numerical experiments are carried out to put in practice our theoretical findings
-
The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the Probability density function
'Elsevier BV', 2018Co-Authors: Calatayud Gregori Julia, Cortés J.-c., Jornet Sanz MarcAbstract:[EN] This paper deals with the damped pendulum random differential equation: (X) over double dot(t)+2 omega(0)xi(X) over dot(t) + omega X-2(0)(t) = Y(t), t is an element of [0, T], with initial conditions X(0) = X-0 and (X) over dot(0) = X-1. The forcing term Y(t) is a stochastic process and X-0 and X-1 are random variables in a common underlying Complete Probability Space (Omega, F, P). The term X(t) is a stochastic process that solves the random differential equation in both the sample path and in the L-P senses. To understand the probabilistic behavior of X(t), we need its joint finite-dimensional distributions. We establish mild conditions under which X(t) is an absolutely continuous random variable, for each t, and we find its Probability density function f(X(t))(x). Thus, we obtain the first finite-dimensional distributions. In practice, we deal with two types of forcing term: Y(t) is a Gaussian process, which occurs with the damped pendulum stochastic differential equation of Ito type; and Y(t) can be approximated by a sequence {Y-N(t)}(N-1)(infinity) in L-2([0, T] x Omega), which occurs with Karhunen-Loeve expansions and some random power series. Finally, we provide numerical examples in which we choose specific random variables X-0 and X-1 and a specific stochastic process Y(t), and then, we find the Probability density function of X(t). (C) 2018 Elsevier B.V. All rights reserved.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. The authors are grateful for the valuable comments raised by the reviewers that have improved the final version of the paper.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the Probability density function. Physica A Statistical Mechanics and its Applications. 512:261-279. https://doi.org/10.1016/j.physa.2018.08.024S26127951
Tomasz R Bielecki - One of the best experts on this subject based on the ideXlab platform.
-
semimartingales and shrinkage of filtration
Annals of Applied Probability, 2021Co-Authors: Tomasz R Bielecki, Monique Jeanblanc, Jacek Jakubowski, Mariusz NieweglowskiAbstract:We consider a Complete Probability Space (Ω,F,P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F⊂G. On this Probability Space we consider a real valued G-semimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compute the F-semimartingale characteristics of the F-optional projection of X in terms of the G-canonical decomposition and the G-semimartingale characteristics of X. In this paper problem B is solved under the assumption that the filtration F is immersed in G. Beyond the obvious mathematical interest, our study is motivated by important practical applications in areas such as finance and insurance (cf. Structured Dependence Between Stochastic Processes (2020) Cambridge Univ. Press).
Calatayud Gregori Julia - One of the best experts on this subject based on the ideXlab platform.
-
Mathematical methods for the randomized non-autonomous Bertalanffy model
Texas State University, 2020Co-Authors: Calatayud Gregori Julia, Caraballo Garrido Tomás, Cortés López, Juan Carlos, Jornet Sanz MarcAbstract:In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, x(t0, ω) = x0(ω), where a(t, ω) and b(t, ω) are stochastic processes and x0(ω) is a random variable, all of them defined in an underlying Complete Probability Space. Under certain assumptions on a, b and x0, we obtain a solution stochastic process, x(t, ω), both in the sample path and in the mean square senses. By using the random variable transformation technique and Karhunen-Loève expansions, we construct a sequence of Probability density functions that under certain conditions converge pointwise or uniformly to the density function of x(t, ω), fx(t) (x). This permits approximating the expectation and the variance of x(t, ω). At the end, numerical experiments are carried out to put in practice our theoretical findings
-
The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the Probability density function
'Elsevier BV', 2018Co-Authors: Calatayud Gregori Julia, Cortés J.-c., Jornet Sanz MarcAbstract:[EN] This paper deals with the damped pendulum random differential equation: (X) over double dot(t)+2 omega(0)xi(X) over dot(t) + omega X-2(0)(t) = Y(t), t is an element of [0, T], with initial conditions X(0) = X-0 and (X) over dot(0) = X-1. The forcing term Y(t) is a stochastic process and X-0 and X-1 are random variables in a common underlying Complete Probability Space (Omega, F, P). The term X(t) is a stochastic process that solves the random differential equation in both the sample path and in the L-P senses. To understand the probabilistic behavior of X(t), we need its joint finite-dimensional distributions. We establish mild conditions under which X(t) is an absolutely continuous random variable, for each t, and we find its Probability density function f(X(t))(x). Thus, we obtain the first finite-dimensional distributions. In practice, we deal with two types of forcing term: Y(t) is a Gaussian process, which occurs with the damped pendulum stochastic differential equation of Ito type; and Y(t) can be approximated by a sequence {Y-N(t)}(N-1)(infinity) in L-2([0, T] x Omega), which occurs with Karhunen-Loeve expansions and some random power series. Finally, we provide numerical examples in which we choose specific random variables X-0 and X-1 and a specific stochastic process Y(t), and then, we find the Probability density function of X(t). (C) 2018 Elsevier B.V. All rights reserved.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia. The authors are grateful for the valuable comments raised by the reviewers that have improved the final version of the paper.Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the Probability density function. Physica A Statistical Mechanics and its Applications. 512:261-279. https://doi.org/10.1016/j.physa.2018.08.024S26127951
Janusz Morawiec - One of the best experts on this subject based on the ideXlab platform.
-
on a refinement type equation
Journal of Applied Analysis, 2008Co-Authors: Rafa L Kapica, Janusz MorawiecAbstract:Let ( ;A;P ) be a Complete Probability Space. We show that the trivial function is the unique L 1 -solution of the following re- nement type equation f(x) = Z j' 0(x;!)jf('(x;!))dP (!) for a wide class of the given functions '. This class contains functions of the form '(x;!) = (!)x (!) with1 < R logj (!)jdP (!) < 0.