Showing papers in "Stochastic Analysis and Applications in 1994"
TL;DR: In this paper, a generalization of the Filippov theorem for stochastic differential inclusions is presented, with an application to linearization of differential-inclusions and to infinitesimal behavior of solutions.
Abstract: We prove a generalization of the Filippov Theorem, [4], for stochastic differential inclusions, and present an application to linearization of differential inclusions and to infinitesimal behaviour of solutions
73 citations
TL;DR: In this paper, the existence and regularity of mild solutions of a class of nonlinear stochastic differential inclusions on Hilbert space was studied and the drift term contains a generator of a C 0 analytic semigroup in addition to the multivalued drift.
Abstract: In this paper we present some new results on the existence and regularity of mild solutions of a class of nonlinear stochastic differential inclusions on Hilbert space. The drift is multivalued and the diffusion is single valued but both nonlinear admitting differential operators unlike in [3]. The drift term contains a generator of a C 0 analytic semigroup in addition to the multivalued drift
57 citations
TL;DR: In this article, the authors extend the result proved by Jurdjevic and Quinn on the stabilizability of deterministic control systems to the feedback stabilization of control stochastic differential equations.
Abstract: The purpose of this paper is to extend the result proved by Jurdjevic and Quinn [6] on the stabilizability of deterministic control systems to the feedback stabilization of control stochastic differential equations
29 citations
TL;DR: In this paper, sufficient conditions to get exponential stability for the sample paths (with probability one) of a nonlinear monotone stochastic Partial Differential Equation (PDE) are proved.
Abstract: Sufficient conditions to get exponential stability for the sample paths (with probability one) of a non–linear monotone stochastic Partial Differential Equation are proved. In fact, we improve a stability criterion established in Chow [3] since, under the same hypotheses, we get pathwise exponential stability instead of stability of sample paths
20 citations
TL;DR: In this article, a class of multifunctions is introduced and a random fixed point theorem for pairs of measurable multifunctions belonging to this class is proved, and the result is then used to study the existence of solutions for the class of random operator equations.
Abstract: A Class of multifunctions is introduced and a random fixed point theorem for pairs of measurable multifunctions belonging to this class is proved. The result is then used to study the existence of solutions for a class of random operator equations
16 citations
TL;DR: In this article, a necessary and sufficient ergodicity criterion for queueing processes is also established for a class of compound point processes and their behaviour about some critical level is analyzed, where the input process is assumed to be semi-Markov modulated process with a kind of feedback dependence on states of the system.
Abstract: This paper deals with stochastic processes that are encountered in a wide class of bulk–input and bulk–service servicing systems systems with one server of random capacity. It generalizes most of the known stochastic bulk queueing models. The analysis is based on recent results for a class of compound point process and their behaviour about some critical level which in this paper is assumed to be random and state dependent The input process is assumed to be semi–Markov modulated process with a kind of feedback dependence on states of the system. The author uses the notion of modulated and output processes. A necessary and sufficient ergodicity ergodic theorems for input and output processes. A necessary and sufficient ergodicity criterion for queueing processes is also established. Stationary distributions of the processes are computed by using analysis for semi-regenerative processes. Various characteristics of related processes (idle and busy periods and intensity of the input and output) are obtained, ...
12 citations
TL;DR: In this paper, necessary and sufficient conditions for existence of equivalent martiangles measures in semimartingale models for the pricing of contingent claims are derived for the case of this paper.
Abstract: In this paper, necessary and sufficient conditions for existence of equivalent martiangles measures in semimartingale models for the pricing of contingent claims are derived
10 citations
TL;DR: In this article, the authors derive sufficient conditions for the existence of stabilizing feedback laws for control stochastic bilinear systems and apply these results to the stabilization of a class of non-linear Stochastic differential systems.
Abstract: The purpose of this note, is to derive sufficient conditions for the existence of stabilizing feedback laws for control stochastic bilinear systems and to apply these results to the stabilization of a class of nonlinear stochastic differential systems. The method used in this paper rely on the stochastic Lyapunov machinery
9 citations
TL;DR: In this paper, it was shown that the pathwise uniqueness of the solution implies the convergence in the strong sense of the Caratheodory approximation to the solution of a stochastic differential equation.
Abstract: In this paper we study the Caratheodory approximation for the solution of a stochastic differential equation. It is shown that the pathwise uniqueness of the solution implies the convergence in the strong sense of the Caratheodory approximation to the solution.
9 citations
TL;DR: In this article, the class of harmonizable processes and fields is defined and a classification of these fields is obtained based upon the smoothness properties of their covariances, and it is shown that there exist non-trivial harmonizable isotropic fields which satisfy the Laplace operator in the L 2-sense.
Abstract: The class of harmonizable processes and fields are a natural extension of the class of stationary processes and fields. Random fields admit an additional property called isotropy. The classical spectral and covariance representations for stationary isotropic random fields are extended to the harmonizable isotropic case. A classification of these fields is obtained based upon the smoothness properties of their covariances. In contrast to the stationary case, it is also shown that there exist non-trivial harmonizable isotropic fields which satisfy the Laplace operator in the L 2-sense
8 citations
TL;DR: In this article, the large deviation principle for stochastic evolution equation driven by gaussian martingales taking values in duals of nuclear Frechet spaces is presented for the case of Gaussian Martingales.
Abstract: This paper presents the large deviation principle for stochastic evolution equation driven by gaussian martingales taking values in duals of nuclear Frechet spaces
TL;DR: In this paper, Ito's stochastic differential equation with unbounded nonlinear "drift" opterator and Hilbert-Schmidt class "diffusion" operator is considered.
Abstract: We consider Ito's stochastic differential equation with unbounded nonlinear “drift” opterator and Hilbert–Schmidt class “diffusion” operator. Existence and uniqueness theorems, and Makrov property of the constructed stochastic process are proved
TL;DR: In this paper, a class of stochastic systems of particles with variable weights is studied and the corresponding empirical measures are shown to converge to the solution of the spatially homogeneous Boltzmann equation.
Abstract: A class of stochastic systems of particles with variable weights is studied.The corresponding empirical measures are shown to converge to the solution of the spatially homogeneous Boltzmann equation. In a certain sense, this class of stochastic processes generalizes the “Kac master process”
TL;DR: In this paper, the Langevin algorithm in R n was studied by means of the theory of ultracontractive semigroups and of the corresponding logarithmic Sobolev inequalities.
Abstract: We study the Langevin algorithm in R n by means of the theory of ultracontractive semigroups and of the corresponding logarithmic Sobolev inequalities. Our results generalize to diffusions in R n the estimates obtained by Holley and Stroock (Commun. Math. Phys. 115 (1988), 553-569) for the case of simulated annealing on a finite (or at least compact) state space
Journal Article•
TL;DR: In this paper, a comparison theorems for stochastic differential inequalities of ordinary and parabolic type are derived for reaction-diffusion processes with random sources, and the question whether or not those sources have an influence on t he blow up of the solutions is investigated.
Abstract: Comparison theorems for stochastic differential inequalities of ordinary and parabolic type are derived. Two methods are proposed, one exploiting the diffentiability of the solutions at the starting time and one based on Gronwall's inequality. The results are then applied to reaction–diffusion processes with random sources. Emphasis is put on the question whether or not those sources have an influence on t he blow up of the solutions
TL;DR: In this paper, the authors considered the optimal control problem for a discrete stochastic singular system and showed that the interpolated sequence converges weakly to a singularly controlled diffusion process.
Abstract: Optimal or approximately optimal control problem for a discrete stochastic singular system is considered. The driving wide band noise is state dependent and the dynamics is non–smooth. It is shown that the interpolated sequence converge weakly to a singularly controlled diffusion process. The optima or “nearly optima” controls of the limit diffusion are shown to be “nearly optima” for the actual system. Weak convergence analysis is used via a combination of Skorohod and pseudo path topology. Discounted cost criterion is considered
TL;DR: In this paper, the covariance function of the backward and forward recurrence times in an ordinary renewal process for both the time dependent and the steady state cases is obtained and special cases are investigated.
Abstract: The joint complementary distribution function is used to obtain the covariance function of the backward and forward recurrence times in an ordinary renewal process for both the time dependent and the steady state cases. Hence, a closed form expression for the steady state correlation of the backward and forward recurrence times is obtained and special cases are investigated
TL;DR: In this paper, the authors consider a discrete dynamical system where a stationary ergodic Markov chain with state space is a bounded C1 map and give conditions under which the Lyapunov spectrum associated with this system reduces, with probability one, to the top Lyapeunov exponent.
Abstract: In this paper we consider the discrete dynamical system where is a stationary ergodic Markov chain with state space is a bounded C1 map, and We first give conditions under which the Lyapunov spectrum associated with this dynamical system reduces, with probability one, to the top Lyapunov exponent. We then investigate the relationship between this exponent and the moment Lyapunov exponents of the system and give a basic large deviation result
TL;DR: In this paper, a simple and effective technique is described and tested for reducing the variation in estimated expectations of functions of function of solutions of stochastic differential equations (SDEs).
Abstract: A simple, effective technique is described and tested for reducing the variation in estimated expectations of functions of functions of solutions of stochastic differential equations. The technique is implemented with extrapolated Euler method for numerical solution of stochastic differential equations
TL;DR: In this paper, three Markov models for identical unit parallel, k-out-of-n and standby arrangements with common cause failures are presented, and the plots of system reliability and mean time to failure are shown.
Abstract: This paper presents three newly developed Markov models for Identical unit parallel, k-out-of-n and standby arrangements with common-cause failures. Generalized expressions for system reliability and mean time to failure are developed. The plots of system reliability and system mean time to failure are shown
TL;DR: In this article, the authors generalized the concept of Compound Point Process (PP) to account for situations in which the compound events are described by a stochastic process rather than a random variable.
Abstract: The Concept of Compound point(or counting)process is generalized to account for situations in which the compound events are described by a stochastic process rather than a random variable. Quasi–closed form expressions for the mean and the variance of this extended compounded point process are obtained in terms of the first two moments of the underlying point process and of the process describing the compound events. An expression for the higher moments is also obtained. The results are applied to obtain the mean and variance of the number of busy channels in a ppx/G/∞ queue. (PP=point process) which generalises results of the M(t)x/G/∞ and GIx/G/∞ queue. Other applications include the derivation of the first two moments of the total backlog and of the revenues from telephone traffic in a PP/G/∞ queue. Finally, a special empirical model is considered
TL;DR: In this article, the extended compound renewal process, a generalization of the concept of filtered Poisson process, is introduced and its characteristic function is expressible as the solution of a second type Volterua integral equation.
Abstract: The extended compound renewal process, a generalization of the concept of filtered Poisson process, is introduced. It is shown that its characteristic function is expressible as the solution of a second type Volterua integral equation is solved for some special cases. Moreover, the equation is used to find the first moment and a recursive relationship for the higher order raw moment of the process. Finally, several areas of applications to the GIx/G/∞ queue are investigates including the size of the system, the queue output and the total backlog
TL;DR: In this article, the best nonrandom sampling scheme, the two-stage sampling scheme and the optimal sampling scheme are discussed for estimating the success probability of a Bernoulli variable with success probability θ = θ 1 θ 2 using a Bayesian approach.
Abstract: Suppose that for i = 1,2, a Bernoulli random variable with success probability θi is observable from population i. The problem is to estimate θ = θ1θ2 using a Bayesian approach with squared error estimation loss in θ. For estimating θ, the best nonrandom sampling scheme, the two-stage sampling scheme, and the optimal sampling scheme are discussed. It is shown that the two-stage sampling scheme is typically asymptotically optimal, and can improve the Bayes risk (over the best nonrandom allocation) up to fifty percent
TL;DR: In this paper, a necessary and sufficient condition for the existence of an adaptive decision procedure is obtained when the nuisance parameter takes values in a compact topological space and observations (possibly in continuous time) have log-likelihood ratios obeying the large deviatons principle.
Abstract: The multiple hypotheses testing problem is studied when the family of underlying probability distributions involves a nuisance parameter. A necessary and sufficient condition for the existence of an adaptive decision procedure is obtained when the nuisance parameter takes values in a compact topological space and observations (possibly in continuous time) have log-likelihood ratios obeying the large deviatons principle. By definition, an adaptive procedure is asymptotically fully efficient for each value of the nuisance parameter and does not depend on it. The mentioned adaptation condition is illustrated by Gaussian and Markov processes
TL;DR: In this paper, the pathwise stabilizability of a linear infinite dimensional stochastic differential equation through anticipative control is studied under some commutativity assumptions, and the generalization of the deterministic Hautus condition is given and applied to a concrete parabolic SPDE.
Abstract: In this paper the pathwise stabilizability of a linear infinite dimensional stochastic differential equation through anticipative controls is studied under some commutativity assumptions. The generalization of the deterministic Hautus condition is given and it is applied to a concrete parabolic SPDE
TL;DR: In this paper, risk adjustment is proposed to overcome the divergence between the moments and sample path behavior of the stock price process, where a stock with an exponentially increasing expected value and a positive expected rate of return may have a typical sample path which approaches 0 asymptotically.
Abstract: Geometric Brownian motion is one of the most frequently used tools in modelling stock prices. To complete the general equilibrium analysis, the expected rate of return on each stock is usually assumed to be equal to the risk-free rate of interest. However, there is a divergence between the moments and sample path behavior of the stock price process. A stock with an exponentially increasing expected value and a positive expected rate of return may have a typical sample path which approaches 0 asymptotically, so that a serious problem arises in the interpretation of asset markets equilibrium. We suggest that by introducing risk adjustment, it is possible to overcome this problem
TL;DR: In this article, the authors derive the Zakai equation associated with nonlinear filtering problems when the observation process is discontinuous and takes its values in a Riemannian symmetric space.
Abstract: The aim of this paper is to derive the Zakai equation associated with nonlinear filtering problems when the observation process is discontinuous and takes its values in a Riemannian symmetric space. The main tools are the stochastic development and the horizontal lift of manifold–valued cadlag semimartingales
TL;DR: In this article, stopping time and supremum comparisons are made for products of finite sequences of non-negative integrable random variables under various restrictions on the class of distributions governing these random variables.
Abstract: Stopping time and supremum comparisons known as “Prophet inequalities” are made for products of finite sequences of non–negative integrable random variables under various restrictions on the class of distributions governing these random variables. for example it is shown that for X0= constant > 0, and non-nagative integrable random variables, that the expected maximum of the product variables, that the expected maximum of the product sequence is no more that n+1 times the value of the product sequence when stopped by non-anticipating stopping times
TL;DR: In this paper, a two dimensional stochastic process is developed to model exchange rate dynamics, incorporating the non random walk influence of pur-chasing power parity, to synthesise the theories of international trade and foreign currency options.
Abstract: A two dimensional stochastic process is developed to model exchange rate dynamics. We incorporate the non random walk influence of pur–chasing power parity, to synthesise the theories of international trade and foreign currency options. Our results, which include a closed form expression for the transition density function of the exchange rate and an exact formula to price currency options, offer a theoretical framework for further study of foreign exchange markets