Showing papers in "Stochastic Processes and their Applications in 2003"
TL;DR: In this paper, stable-like processes on d-sets are investigated, which include reflected stable processes in Euclidean domains as a special case, and a sharp two-sided heat kernel estimate for such processes is derived.
453 citations
TL;DR: In this article, a priori estimates and prove existence and uniqueness of solutions in L p p > 1, extending the results of El Karoui et al. to the case where the monotonicity conditions of Pardoux (Nonlinear Analysis; Differential Equations and Control (Montreal, QC, 1998), Kluwer Academic Publishers, Dordrecht, pp. 503-549) are satisfied.
403 citations
TL;DR: In this paper, the authors investigated the probability of ruin within a finite horizon for a discrete time risk model, in which the reserve of an insurance business is currently invested in a risky asset.
345 citations
TL;DR: In this paper, a new characterization of excessive functions for arbitrary one-dimensional regular diffusion processes is provided, using the notion of concavity, and a new perspective and new facts about the principle of smooth-fit in the context of optimal stopping are presented.
289 citations
TL;DR: In this article, the authors consider a model in which the numbers of offspring for the individuals are independent, but in each generation only N of the offspring are chosen at random for survival, and assume that if X is the number of offspring of an individual, then P ( X ⩾ k )∼ Ck − a for some a > 0 and C > 0.
194 citations
TL;DR: In this article, the authors deal with the risk-sensitive control, zero-sum and non-zero-sum game problems of stochastic functional differential equations, and they show the existence of an optimal control and, a saddle-point and an equilibrium point for respectively the zero sum and non zero sum games.
183 citations
TL;DR: In this paper, the authors studied the stability of nonlinear stochastic differential equations with Markovian switching and found that the stability is asymptotically stable. But, the authors did not consider the stability in the distribution of the nonlinear differential equations without Markovians.
178 citations
TL;DR: In this paper, the authors consider a system of stochastic equations which models the population dynamics of a prey-predator type and show that the distributions of the solutions of this system are absolutely continuous.
176 citations
TL;DR: In this paper, the authors compare three dependence coefficients expressed in terms of conditional expectations, and study their behaviour in various situations, and give a new covariance inequality involving the weakest of those coefficients, and compare this bound to that obtained by Rio (Ann. Inst. H. Poincare Probab. Statist. 29 (1993) 587-597) in the strongly mixing case.
162 citations
TL;DR: In this article, an integral representation of the fractional white noise as generalized Wiener integral was proposed for fractional Brownian motions BtH with arbitrary Hurst coefficients 0
138 citations
TL;DR: This paper deals with the analysis of the statistical error induced by the Monte Carlo estimation of the transition weights of the quantization tree of the Bally and Pages (2000) algorithm.
TL;DR: In this paper, the authors consider a linear rate equation, depending on three parameters, that model fragmentation and obtain criteria for the presence or absence of loss of mass in the fragmentation equation, as a function of the equation parameters.
TL;DR: In this paper, the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, and convex trading constraints (e.g., incomplete markets and short-sale constraints) is considered, and first-order conditions of optimality are derived, based on a preference independent notion of constrained state pricing.
TL;DR: In this paper, a generalization of the Dirichlet process is introduced, and the concept of n-covariation is defined through a regularization procedure, where the n-variation process of a continuous process is defined.
TL;DR: In this article, the convergence rate of Markov chains under conditions implying geometric ergodicity was studied and bounds for the total variation norm were obtained by evaluating the moments of an appropriately defined coupling time, using a set of drift conditions adapted from an earlier work by Tuominen and Tweedie.
TL;DR: In this article, necessary and sufficient conditions for the equivalence of Volterra Gaussian processes were studied and new proofs, precisions and new theorems for equivalence were provided.
TL;DR: In this article, a new method of approximation based on the cutoff of the small jumps of the Levy process involved is proposed, and the speed of convergence of the approximation is found by using stability of the solutions of SDEs.
TL;DR: In this paper, the consistency and limiting distributions of a class of M-estimators in two-phase random design linear regression models where the regression function is discontinuous at the change-point with a fixed jump size are discussed.
TL;DR: In this article, the robustness of the optimal filter w.r.t. its initial condition is studied by introducing a robust filter, which is exponentially stable and which approximates the optimal filtering uniformly in time.
TL;DR: In this paper, the authors show how to homogenize a semilinear parabolic second-order partial di-erential equation, whose coe6cients are periodic functions of the space variable, and are perturbed by an ergodic di-usion process.
TL;DR: In this paper, the conditional central limit theorem was shown to imply stable convergence of the normalized partial sums to a mixture of normal distributions, and the functional version of this theorem was established.
TL;DR: In this article, the authors considered a completely asymmetric Levy process X and X reflected at 0 and at a>0, and found an expression for the resolvent density of Z.
TL;DR: In this article, the authors derived Karhunen-Loeve expansions for Volterra type processes and applied them to the estimation of drift parameters in stochastic models driven by Volterras type processes using a Girsanov transformation.
TL;DR: In this article, an additive L"evy process in R d with X = {X (t); t ∈ R N} was considered, where X (t ) = X1(t1 )+ ··· + XN (tN ) ∀t ∈ r n; where X1;:::;
TL;DR: In this paper, a conditional limit theorem and conditional asymptotic expansions are considered based on the Malliavin calculus, and the problem of lifting limit theorems to their conditional counterparts is treated.
TL;DR: In this paper, the exact tail behavior of the solutions to certain nonlinear stochastic differential equations driven by Levy motions with regularly varying tails is described and established existence and uniqueness of solutions to these equations.
TL;DR: In this article, a homogenization theorem for the Dirichlet eigenvalues of reversible random walks on Z d with stationary and uniformly elliptic conductances was proved and applied to almost sure convergence of capacities and currents.
TL;DR: In this paper, the Glivenko-Cantelli theorem for the empirical distribution function was proved for the squared residuals and it was shown that the two-parameter empirical process converges to a Gaussian process.
TL;DR: In this article, the authors considered the effect of trimming ergodic sums of their maximal values on the strong law of large numbers for non-negative, non-integrable, mixing stationary processes.
TL;DR: In this paper, a supercritical branching random walk on a rooted tree with random environment is studied, where both the branching and the step transition parameters are random quantities, and the conditions for strong recurrence and transience are presented.